IN DCINTERNATIONAL NUCLEAR DATA COMMITTEEI.A. Kondurov, Yu.V. Sergeenkov When one is compiling a machine library of nuclear level schemes, the question of the format for presenting

IN DC

International Atomic Energy Agency HTDC(CCP)-72/LN

I N T E R N A T I O N A L NUCLEAR DATA C O M M I T T E E

BULLETIN OP THE DATA CENTRE OP THE LENINGRAD

INSTITUTE OP NUCLEAR PHYSICS (LIYaP)

Issue 2

Translated "by the IAEA

February 1976

IAEA NUCLEAR DATA SECTION, KARNTNER RING 11, A-1010 VIENNA

Reproduced by the IAEA in Austr iaMarch 1976

76-1026

INDC(CCP)-72/LN

BULLETIN OP THE MTA CENTRE OP THE LENINGRAD

INSTITUTE OP NUCLEAR PHYSICS (LITaP)

I s s u e 2

Translated by the IAEA

February 1976

UDK 002.6539-14

CHOICE OF FORMAT FOR THE PRESENTATION OFDATA ON NUCLEAR STRUCTURE

I.A. Kondurov, Yu.V. Sergeenkov

When one is compiling a machine library of nuclear level schemes, the

question of the format for presenting the data naturally arises. For a

complete description of the properties of the excited states of a nucleus

it is sufficient to know the energy of the levels, their spins and parities,

the electric and magnetic moments, and the partial widths of the processes

determining the formation and decay of these states. Such data are needed

both for fundamental research (comparison with predictions of different

nuclear models) and for applied research (calculations of radiation

intensities, etc.).

Recently, it has been proposed a number of times that the ENDF and

EXFOR formats for neutron data be adapted for data on nuclear structure [l].

Furthermore, the Nuclear Data Group at Oak Ridge is already using a format

designed especially for describing nuclear level schemes [2]. The evaluated

data published in Nuclear Data Sheets are presented in this format. It has

been sufficiently formalized, but at the same time it offers the possibility

of expanding the list of described quantities, which means that it can also

be used for presenting the results of practical work on the structure of

excited nuclear states.

The LIYaF Data Centre has attempted to use this format both for the

evaluated schemes of excited nuclear states and for the results of individual

practical studies. Evaluated characteristics of the levels of the P

nucleus and data from the work of V.L. Alekseev et al. [3] on the scheme of

the excited states of Cs, obtained from the reaction Cs(n,y) Csf are

presented in this format by way of example.

A detailed description of the format is given in Ref. [2]; here we

give the information necessary for understanding the tables. A set of data

- 2 -

describing level properties determined experimentally or estimated on the

basis of many reports and the transitions between them consists of a sequence

of punched cards to each of which one row in a table corresponds. There are

several types of card with a fixed format, certain punched card columns

corresponding to each recorded quantity. The set must start with an identifi-

cation card indicating the type of data (reaction, decay, gamma transitions,

etc.) and must end with a blank card. The cards used carry the following

information (with errors where these are known):

Q - binding energy of neutron in nucleus;

L - level energy, spin, parity and lifetime;

G - gamma transition energy, relative intensity and multipolarity;

N - normalization factor for converting relative to absolute

gamma transition intensity;

I - data on K-, L- and M-conversion coefficients.

Commentaries relating to the rows of the table are given on a C card in

free text. If the need arises to record data not defined by the card

description, use is made of additional cards (numbered from 2 to 9) on

which these data appear in textual form. For example, MOMMI = + 1.13167 6

in the second row of the table means that the magnetic moment of the ground

state of 31P = + (1.1316? - 0.00006).

When necessary, the format of cards is redefined by means of an P card.

In Ref. [ l ] , the I card is not defined; it became necessary to introduce i t ,

however, in order to describe the data on internal conversion electrons

contained in Ref. [3]. In the F card, for describing the I card use was made

of the designations a^, a , a^, a« - EKC, ELC, EMC and ENC adopted in Ref. [2];

DEKC, DELC, etc. denote the errors associated with the corresponding quantities

in the units of the last sign.

The last columns of the cards are used for references to commentaries,

for indicating doubtful levels and transitions, and - in the case of G cards -

for identifying coincidences of a gamma transition with the preceding and

subsequent cascades.

When the experimental results of practical work on nuclear structure are

presented in this format, difficulties arise in connection with the recording

of multiparameter tables - for example, the intensities of gamma-gamma

coincidences. Similar difficulties in representing multiparameter distributions

- 3 -

are a l so inherent in the two other formats mentioned [ l ] . With appropriate

refinement, however, the format adopted by the Nuclear Data Group at Oak

Ridge can serve as a bas i s both for c rea t ing an in t e rna t iona l f i l e of

evaluated data on nuclear s t r u c t u r e and for the establishment of l i b r a r i e s

containing the r e s u l t s of p r a c t i c a l work.

REFERENCES

[ l ] PEARLSTEIN, S . , INDC(tfDS) - 6l/W+spec. (1974) 20.

[2 ] Nuclear S t ruc tu re Data P i l e , INDC(in)S) - 6l/W+spec. (1974) 20.

[3 ] ALEKSEEV, V.L. et a l . , p repr in t LIYaP-121, Leningrad, 1974.

- 4 -

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- 10 -

UDK 539.166

0+ STATES AND ELECTRIC MONOPOLE TRANSITIONS INATOMIC NUCLEI

IT. A. Voinova

Much experimental and theore t i ca l work has been devoted to the study of

0 s t a t e s in atomic nucle i , and the in te res t in them i s undoubtedly growing.

In particular-, i t i s known from experiments tha t for many deformed and

t r a n s i t i o n nuclei there are two - sometimes even three •- 0 s t a t e s below the

t r a n s i t i o n energy. There i s at present no single theore t ica l descr ipt ion

of the various 0 exci ta t ions in nucle i . A pa r t i cu la r ly large number of

d i f f i c u l t i e s a r i ses when one i s describing 0 exci ta t ions near and above the

t r a n s i t i o n energy. Many studies have been done of the cha rac te r i s t i c s of

e l e c t r i c monopole t r a n s i t i o n s . This i s understandable, for one obtains

considerable information about the form of the nucleus and ite s t ruc tu ra l

details.

It is known that EO transitions are purely a penetration effect. They

are non-aero only when a transition is accompanied by a change at the surface

of the nucleus - i .e . when calculating the probability of such transitions

one cannot use the adiabatic approximation. In nuclear models where the

form of the nucleus is fixed, EO transitions are strictly forbidden. EO

transitions can occur between nuclear states ha,ving the same spin and parity.

If I -f 0, Ml and E2 components usually blend in with the EO component. In

the investigation of transitions of the type I "• 1 for 1 ^ 0 , it is not the

absolute value of the monopole component which is important but that infor-

mation about the structure of the nuclear levels which can be derived from

study of the matrix elements of the monopole transition.

Several authors [l-4J have tried to systematise the experimental and

theoretical information about excited states of the 0 type and electric

monopole transitions. However, Refs [l~3] contain information only about

deformed nuclei, while only the probabilities of electric raonopole transitions

are considered in Ref. [4]. In the present paper we have collected - from

reports published up to the start of 1975 - and systematized experimental

data on 0"*" states and the characteristics of electric monopole transitions

- 11 -

for all even-even nuclei; the information presented in Ref. [4] is also

included here. We present the energies of 0 states and the probabilities

of Coulomb excitation of levels from which EO transitions have been observed.

As regards the energies of 0 levels, we usually indicate the papers in

which the level was first reported and the latest, most reliable data; as

••egards the probability of E2 transitions, we present only the latest

results. The table contains also values of the ratio of probabilities of

EO and E2 conversion transitions: q = W (EO)/W (E2). If the ratio ofe e

the K-conversion electron intensity of an EO transition to the gamma component

intensity of an E2 transition has been measured, the table contains values

for (i . = L^EO)/! (E2). It should be noted that q is usually obtained from

measurements of the conversion coefficients; from measurements of the

angular correlation of conversion electrons, on the other hand, it is possible

to obtain q, which determines the ratio of the amplitudes of the EO and E2

components of the conversion electrons. Since ey angular correlation measure-

ments enable one to determine not only the value but also the sign of q, the

table contains also values of q with the sign in cases where they have been

measured. From the experimental value of q it is possible to calculate the

value of the nuclear matrix element of penetration:

In a mixed EO + Ml + E2 transition, the Ml conversion process may-

depend on the penetration effect. The table contains values of X.

characterizing the penetration effect in the Ml component. Lastly, the table

contains values of the dimensionless parameter X introduced by Rasmussen

X = 2,54 I0 A

0+-*. 2+) n (Z,k)

E(SO, 0+ — 0+ ) = e2 p 2 R4

R - radius of nucleus,

0, - 0 + level with number k,

0.. - ground state of nucleus.

- 12 -

For transitions between zero-spin levels, the table gives the ratio

lere the spins of the k-th and the 1st level are equal. Both these ratios

re denoted by X in the table. If experimentalists have determined the

atios of the probabilities of other EO and E2 transitions, they are specially

oted in the table. For the O.586 MeV EO + E2 transition of the 0.931 MeV 2+

3vel of Gd, for example, the ratio B(E0)/B(E2, 22->0l) is given. This

enotes the relation between the given probability of an EO transition from

tie 2 level in question to the level of the fundamental rotation band 2

id the B(E2) value of a transition from a second excited state of type 2152

0 the ground state of the Gd nucleus. Occasionally we have determined

tie ratio of B(EO) to the sum of the given probabilities of E2 transitions

rom the level under consideration to the level of the fundamental rotation

and. Such ratios appear as B(E0)/sB(E2)in the table.

The table has 11 columns:

1-3 - Isotope

4 - Level energy, in MeV

5 - Quantum characteristics of level

6 - Energy of transition in question, in MeV

7 - Multipolarity of transition

8 - Quantity represented:

QSQ - q2,

Q - q,

K(E0)/lG(E2) - (ik,

RHO - Q(EO),

X - X,

E -ifX,B(E2)U - B(E2)T,

LAMBDA - X.

9 & - Numerical value of the quantity and the associated error,10 in units of the last sign. The numbers in parentheses

denote an order of magnitude; for example, 1.78(-2) means1.78 x 10~ . Values of B(E2) are given in e2 • barn2.

11 - Work in which given quantity is measured.

- 13 -

Experimental data on Gd are presented for purposes of illustration.

The levels are given in order of rising energy; the transitions from each

level are given in order of decreasing energy.

Experimental data on 0 states and electric monopole transitions in

even-even atomic nuclei are recorded on magnetic tape at the LIYaF Data

Centre.

REFERENCES

[l] DZHELEPOV, B.S., SHESTOPALOVA, S.A., Proc. Dubna Symp. Nucl. Instr.

1968, IAEA, Vienna (1968) 39.

[2] BJORNHOLM, S., Nuclear excitations in even isotopes of the heaviest

elements, Thesis, Munksgaard, Copenhagen (1965).

[3] PYATOV, N.I., preprint P4-5422, Dubna (1970).

[4] ALDUSHCHENKOV, A.V., VOINOVA, N.A., Nucl. Data Tables, A U (1973) 299.

[5] RASMUSSEN, J.O., Nucl. Phys., 19 (i960) 85.

6J

f>4

ft*64

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64

64

64

6464646464

64

646464

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6464

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64

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64

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64

6464

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CDr,oGDGRCDGO

CDCOCDCOCD

cnCDGDCOCDCDCDCDCOCDCDCOCOGDCDCOCDCOGOGOCDCDCDCDCDCDGD

cnGDGDGDGD

15 2 s > 6 \ 5

1 5 2 0»f>i5

152 O.M5152 0«MS152 0«6i5

15 2 o • 9 3 1

15 2 0•9 3 1

152 o«'3115 2 0 • <> 3 115 2 0 • 9 a 115 2 0 • <* 3 1152 (152 (152 t152 (152 (152152152152152152

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) . 9 3 1

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) • 9 3 1

) • 9 3 1.93T

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l«0'*8

1-048

1 .048

1*048

1.048

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•048

1 • 04B

I«n4fl

1 * 0 4 8

1.053

1 • lO"3

t • 2 8 2

I . 2 8 2

a»0*0*0*2*2*2*2*2*2*2 +

2*2*2*2*

0*0*0 +

0*

o*-0*0*

a*0*0*

n*0*

0*

0*

0*2*4*4»

1 . 3 1 R 4 2 *. 3 T B 4 2 •

. 3 1 B 4 2 •

. 3 m i

.484•4n4• flfv2

• R 6 2> . 7 a 1

(2*

(o*)(0.)2*2*io*>

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0 . 6 1 5

O . 6 I 5

0 . 6 1 5

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0 . 5 R h

0 . 5 P- 6

r,. 5 R 6

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1 .048

1 .0481 .04B1 .0481 ,0«H1 . 0*t)

1 . 0 « B

1 .04rt

1 . f)4B

1 . 0 4 8

EO£()EOEOEOEo*E 2

Eo + 2r 0 * M 1E o * M 1

F- 0 * E 2

Eo*E 2

E 0 * E 2

£ 0 * E 2

E Q * E 2

E 0 * E 2

E 0 * E 2

EOEGEQ

EoEOEOEOEOEl)COC

0 . 4 3 2 5 E o0 . 4 3 2 5 E rj

0 * 7 6 4

D . 5 2 6 <

E0«.E2

5 E o * E 2fl , 5 2 6 9 E 0 * E 2

0.9740 .974

l E o * E 2

| E 0 * E 2

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0.38/f

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EOft , 5 4 3 7 E o * E 2

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E a

l K ( F . 0 ) / I c t E 2 )XXXX

! K ( E 0 ) / Kasa

: E 2 )

B ( K o ) / B ( E 2 , 2 2 - o 3 )B ( E 0 > / f i ( E 2 , 2 2 " o l )B ( E Q ) / R ( E 2 , 2 2 - 0 2 )

1 K ( E 0 ) / 1 0 ( E 2 )X

X

X

XB ( E n - y 3 - n 2 ) / B ( E o . 0 3 - 0 1B ( E Q ) 0 3 - 0 2 ) / B ( E o , 0 3 - 0 1P ( F - O i 0 3 - n 2 ) / B ( E O i 0 3 - 0 1B U r i » 0 3 - n 2 ) / B ( E 2 i 0 3 - 0 2 ;B ( E 0 ) / B ( r . 2 , n 3 - 2 2 )t K ( E 0 ) / I G ( E 2 )B ( E 0 ) / B ( E 2 , 0 3 - 2 2 )

nso! K ( E 0 ) / I f i ( E 2 )XI K ( B O ) / I C ( E 2 )X

] K < g O ) / ! C ( E 2 )X

1 K ( E 0 ) / 1 a < E 2 )

X .

1 . 3 1 ( - 1

1 . 3 ( - 2 )

1 , 2 ( - 2 )

4 . 2 ( 0 )

>= 3 , 5 5 < - l> = - 1 . 3 8 ( * ;1 , 1 ( n )H - l )S ( - 2 )6 . n (• 2 )5 . 5 ( - 3 )2 . 8 < o )1 . 5 ( - 2 1

> * 2 . 5 ( - l )6 . 7 ( - 2 )> 6 , 2 < - 2 >8 , 7 ( - 2 )2 . R ( 4 l )6 . 3 ( • \)5 . 9 ( 4 1 )1 . 5 ( - 2 )1 . 2 5 ( - 4 )

2 . 5 ( r )7 . 3 ( ^ 2 )2 . 3 4 ( - !2 . 4 < - 3 ,8 . R ( . 2 )3 . 6 ( - 1 ,

3 . K . I )

9 . 3 ( - 1 )

i r

11

i n<c I . 1 ^ 5 ( 0 )<= * 2 . 5 ( * 1 )

6 0 T 0 f; .V6 1 H fl 1 7

15

245

1172331 1Ins

7 1 Z 0 0 5 ! 37 1 Z 0 0 S i 3

7 2 K fl 0 f, ; 3

?2Kfl0fc i 5

6 0 T 0 n 3 •> 9

6 7 G R 0 5 ' 57 1 Z 0 0 5 1 36 J T 0 0 3-196 7 G R 0 5 1 56 7 a R n 5 ) 57 1 F L 1 2 i S

7 I Z 0 0 .5 1 3

6 1 H fl 1 7 .-; 8

7 1 Z 0 0 5 1 36 0 T 0 0 3 •'! 96 1 H R\ 7 > 86 7 r. ft 0 5 •' 56 ?r. DO 5 !

7 1 2 0 n 5 I 37 1 Z 0 0 5 1 37 2 E L 0 4 •' 3

7 1 Z 0 0 5 i 37 1 Z 0 0 5 I 37 12 0 0 5 137 1 Z 0 0 5 I 37 1 Z 0 0 5 1 37 1 Z 0 0 .5 i 369/100 10 96 7 G R 0 .S <1 57 1 Z 0 0 5 : 37 1 Z 0 Q 5 i 36 7 G R 0 fi I! 5

- 15 -

UDK 539.166.3

TABLE OP NUCLEAR LE\TEL LIFETIMES

Eh.E. Berlovich, L.A. Vajshnene, I.A. KondurovYu.N. Novikov, Yu.V. Sergeenkov

The table of l i fet imes includes experimental data obtained from direct

and indirect measurements of the l ifet imes of excited s ta tes of atomic nucle i .

I t is a continuation of the table contained in Ref. [ l ] . The data have been

systematized on the basis of an information re t r i eva l system developed by the

Data Centre of the Leningrad Ins t i tu te of Nuclear Physics (LITaP) [ 2 ] ,

Tables with data published up to the s t a r t of 1974 have been issued in a

LIYaP preprint [ 3 ] .

The table contains values for the l ifetimes of bound s ta tes - i . e . of

nuclear levels below the binding energy of a peripheral proton and a neutron

in the nucleus and, in the case of l ight nuclei (Z "S 20) r below the alpha

par t i c l e binding energy.

The table has nine columns. Column 1 gives the atomic number of the

element and column 2 i t s chemical symbol; column 3 gives the mass number;

column 4 gives the energy of the excited s t a t e in MeV; column 5 indicates

the quantity measured (the ha l f - l i f e T i f the level width P, or the reducedz

probability, B(EL), of an electric transition of multipolarity L).

The reduced probabilities of transitions, B(EL), in the table correspond

to transitions connecting ground with excited nuclear states. The values

of B(EL) are given in the following units: e a = e * (10 ^ ) cm . The

EB(EL) quantities denote partial reduced probabilities of transitions.

The level width associated with a transition to the ground state of

a nucleus is denoted by PO. The partial width in respect of the gamma

discharge of a level is represented by PG and the total width by G. The

•G in front of the TO denotes a statistical factor and J denotes the level

spin.

The half-life (TjJ, level width (P) and reduced probability B(EL) data2

are presented in column 6, where the first number is the measured quantityand the number in parentheses is the order of magnitude. The values of the

level half-lives is in seconds and P is in eV.

-16-

Column 7 contains the measurement error in the last significant figures

of the result; thus, 5.2O(- 12)28 means (5.20 - 0.28) * 10~12.

The experimental method by which the value in column 7 is obtained is

indicated in column 8 as follows:

BH - time measurements, including observation of the decline in

radiation activity, comparison of the number of excited

nuclei with the number of excited nucleus disintegration

events, pulsating beam method, oscilloscope and long-range

alpha methods, method of delayed coincidences of electrons

and gamma rays with gamma rays, and microwave method.

KB - Coulomb excitation of nuclei by charged particles and heavy

ions.

P4 - Particle scattering. This sympol covers work on the

inelastic scattering of heavy particles and of electrons.

PP - resonance scattering of gamma rays by nuclei.

M - M*<5ssbauer effect measurements.

fl - Doppler effect; measurements of line broadening and of

"weakening of the Doppler shift11 and measurements - by

means of the Doppler shift - of the velocities of recoil

nuclei.

II - recoil nucleus method with measurement of the recoil distance

(plunger method).

The cited literature is presented in column 9«

An automatic table print-out sample is presented on the next page.

REFERENCES

[ l ] BERLOVICH, Eh.E., VASILEHKO, S.S. , NOVIKOV, Yu.N., Lifetimes of excited

s ta tes of atomic nuclei ( in Russian), "Nauka" (1972).

[2] KONDUROV, I .A., PETR07, Yu.N. et a l . , in "Bullet in of the LIYaF Data

Centre11, issue 1, Leningrad (1974) 19.

[3] BERLOVICH, Eh.E., VAJSHNENE, L.A. et a l . , preprint LIYaF-145,

Leningrad (1975).

- 17 -

3335333355

55556666777777777777777777777777777

888888888888888888888

LILILILILILILILIBBBB8BbCCCCK

n

N\NNKNNNNNNNNNNNNNNNKN

N000000000000000000000

667777781011111111111 1121214

141314141 4141 U1414141 UH14-141414151515151515151 7171717171616',6161616181818181818181818181818181818

2.1803.5600.4770.4770.4770.4 7 790.4/80.9B10.7172.1202.1202.1202.1404.4404.4404.43015.1096.0^06 . 8V

2.3102.3102.313.95

3.9504.9104 .915.1105 . 6 V 05 .6905.6V5 . S 3 06.?66.447.3008.3108.5/09.0509.1529.2209.9301.8501 .9072.5263.2043 . 6296.056 . 1 i

6.929.8510.3411 .521 .9801 .9821 .982163.5503.5533.555073.6303.6J23.6323.654503.9203.S>2064.4504.45615 . C V 8 5

B<E2)rT1/2T1/2T1/2B(E2)BCE2)T1/2

TW2rTl/2T1/2Tl/2T1/2

rT1 12

rT1/2T1/2

rTl/2T1 12T l / 2Tl/2T1/2T1/2T1/2T1/2T1/2Tl/2T1/2T1/2Tl/2T1/2Tl/2T1/2T1/2T l / 2T l / 2T l / 2T1/2T1/2T1/2T l / 2T1/2T W 2T1/2T1/2

rrrrTl/2T1/2Tl/2T1/2Tl/2T1/2T1/2T l / 2T1/2Tl/2Tl/2

T1/2Tl/2Tl/2T1/2

5.5(-3)6.53.8(-U)< 7(-14)5.5C-14)7.4(-4)8.3(-4)9.7C-15)> 4 . U - 1 3 )2.3C-1)2.0C-15)< 6 , 9 ( - 1 4 )< 7 ( - U )< 6 . 9 ( - U )5 . 3 C - 1 )< 3 . 5 < - 1 4 )3.70(*1 )< 6 . 9 ( - U '•

2 . 5 ( - H )3.615C+4)5.2C-14)< 6.9<-14)7 . 9 (•• 1 4 )

< 1 .9(-1<O< 1 .4C-13)< 1 . 4 ( - 1 3 )

< 1 ,9(-U)> 6.91-1?)< 8.3C-15)< 6 . 9 ( - U )< 1.5(-U)> 6.9C-12)1 .40(-13)4 . i, ( -1 3 )< 6.9C-14)

< 6.9C-U)< 6.9C-U)< 6.9(-14)< 2.7(-U)< 8.9<-14)< 6.9C-U)> 2C-12)> 3(-12)> 2(-12)< 2C-12)> 1(-12)6,7(-11)1 ,84<-i1>1 .30('1)8.8(-3)5.6C-8)6 . 1 ( - 1 >2 . 2 5 ( - 1 2 >2.25(-12)2.0(-12)< 5<-12)> 3.5C-12)> 3C-12)1 .69(-12)1 .01 C-12)9. 2(-13)9 . 2 f - 1 3 )1.0 C-13 *1.7(-1i)< 3.5C-14)4 . 5 ( - U )4 . 3 ( -1 ft )

+24-177

17163

9B

21

11

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13

2

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72BF01787 2 N y 0 1 7 5

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7 2 R E 0 <> 7 072N/017573HA02H97 Z K V 0 1 7 5

?3l-UC28973HA02W972ST035372ST03S?72ST03537 2 S T 0 3 5 372ST035372ST035372ST0353738E007973BE0079733E007973BE00797J8E007O

7<EI0?U73ER061 7733C060973BE060973BE0609'3OE023273OL223973MC00137 3 6 1.2 2 3 973OL223973MC001373OL223973OL22J973WA0418?3WA04i87 3 C L 2 2 3 97'iOii?.l97301.223973OL223V73OL22iy73OLF.23?

- 18 -

UDK 539.16

TABLE OP EXPERIMENTAL (ABSOLUTE) VALUES OF THE MOMENTSOP GROUND AND EXCITED NUCLEAR STATES

M.P. Avotina, A.V. Zolo tav in

The purpose of t h i s work i s t o b r i n g t o g e t h e r and keep up t o da te a

f i l e wi th as much da t a as pos s ib l e on t h e moments of ground and exc i t ed

nuclear states, so as to save the time of experimentalists and indicate

a number of problems s t i l l to be solved. The file also contains the results

of old work, since they have been recalculated in different compilations on

the basis of different assumptions, which has created the impression that

one is dealing with independent measurements. The necessity of such a

detailed approach also follows from the fact that the compilations published

in recent years have contained either information about nuclei obtained by

some single method [ l ] or material collected for only a group of nuclei [2, 3]

- or have contained virtually no Soviet results [4].

In the table are presented experimental (absolute) values of nuclear

moments. The values published outside the Soviet Union before 1972 are

taken mainly from Refs [2, 4-13]. In the case of Soviet sources, Refs [14

and 15] were used in part. Most of the data from Soviet journals is included

in such a system for the first time.

The structure of the file can be understood from the following table,

which contains ten columns:

1-3 Isotope

4 Level energy, in MeV

5 Level lifetime

6 Designation of quantity represented:

I level spin,

MU magnetic dipole moment in units of nuclear magnetons(in the table all MUs are corrected for diamagneticeffect),

Q observed nuclear quadrapole moment, in e • barn,

MU3 nuclear octapole magnetic moment, |i, = Q, in nuclearmoments * barn,

M7 magnetic moment, in nuclear moments * barn ,

G g-factor of state.

- 1 9 -

7-8 Value of quantity and associated error, in units of thelast sign

9 Measurement method and comments concerning correctionsmade (not made)

10 Reference to original or compilation

REFERENCES

[I] CHRISTY, A., HAUSSER, 0 . , Nucl. Data Tables, All (1973) 28l.

[2] International Conference on Hyperfine Interact ions, Uppsala, 10-14 June

(1974).

[3] ZAMYATIN, Yu.S., Jadernye konstanty (Nuclear constants) , issue 14,

Atomizdat (1974).

[4] FULLER, G.H., COHEN, V.W., Nucl. Data Tables, A5_ (1969) 433.

[5] PRISCH, S.E., Spectroscopic determination of nuclear moments, OGIZ,

Leningrad-Moscow (1948).

[6] DZHELEPOV, B.S. , PEKER, L.K., SERGEEV, V.O., Decay schemes of radio-

active nuclei with A > 100 (in Russian), Izd. Akad. Nauk SSSR,

Moscow-Leningrad (1963).

[7] LINDGREN, I . , in Perturbed angular corre la t ions; KARLSSON, E.,

MATTHIAS, E., SIEGBAHN, K., Eds., North Holland Publ. Company,

Amsterdam (1964) 379.

[8] LINDGREN, I . , Ark. Fys. , 2£ (1965) 553.

[9] DZHELEPOV, B.S. , PEKER, L.K., Decay schemes of radioactive nuclei

with A <100 (in Russian), "Nauka", Moscow-Leningrad (1966).

[10] GRODZINS, L., Ann. Rev. Nucl. S c i . , 18 (1968) 291.

[ I I ] SHIRLEY, D.A., in Hyperfine structure and nuclear radiations;

MATTHIAS, E., SHIRLEY, D., Eds. (1968).

[ l 2 ] KHRYNKEVICH, A.Z., P iz . elementar. chas t i t s i atom, yadra (Physics

of elementary par t ic les and of the atomic nucleus) 2 (l97l) 355.

[13] Proc. In t . Conf. Nucl. Moments and Nucl. S t ruc t . , HORIE, H., SUGIMOTO, K.,

Eds., Osaka (1972). Suppl. t o J . Phys. Soc. Japan, 34 (1973).

[14] ARTAMONOVA, K.P., SERGEEV, V.O., Soviet work in nuclear spectroscopy;

bibliographic index 1917-1960 (in Russian), Biblioteka Akad. Nauk

SSSR, Leningrad (1965).

[15] VOROB'EV, V.D., Soviet work in nuclear spectroscopy; bibliographic

index I96I-I965, Biblioteka Akad. Nauk SSSR, Leningrad (1968).

- 20 -

38

33

t &

38

38

44

44

44

44

44

-44

44

44

82

62

02

82

SR

SR

SR

EU

sn

EU

HJ

nor

KJ

KU

RU

PB

FB

P 3

FB

86

86

n £

86

86

101

JO1

101

101

101

101

101

101

208

208

208

202

1.OT72

2.232

2.995

3.003

3.644

0

0

0

0

3

0

0.127

0.127

2.6145

2.6145

2.6145

2.6145

5.5C-1O)

5.5C-1O)

2.U-11)

2.K-H)

2.K-11)

2.K-11)

S

S

S

S

S

S

I

I

I

I

I

I

I

MU

101

lm

MU

I

MU

I

MU

Q

Q

2

4

3

(3)

3

5/2

5/2

-0.69

-0.68

-0.68

0.698

(3/2)

-0.311

3

1.89

-1.0

-1.3

15

3

3

24

26

29

4

6

AC

AC

AC

AC

AC

ESR

0

0

0

MO

IMPACT

IPAC

AC

IPAC

RC

CE

62TAOO68

62YAOO68

62YAOO68

62YAOO68

73BEOO48

52GRO951

55MUO919

55MUO919

65LIO553

66KIO99O

74IfflJO634

66AUO367

66AUO367

65LIO553

72HOOO34

69BA12O5

75GUO2 25

UDK 002.6 - 21 -539.166681.142.2

LIBRARY OF PROBLEM-ORIENTED PROGRAMS FOR SOLVINGPROBLEMS OF ATOMIC AM) NUCLEAR PHYSICS

Y u . I . Kharitonov

The Data Centre of t h e Leningrad I n s t i t u t e of Nuclear Physics (LIYaF)

i s cont inu ing work on the es tabl i shment of a l i b r a r y of problem-or iented

programs for so lv ing problems of atomic and nuc lea r p h y s i c s . The programs

at present available to the Data Centre are listed and described briefly

below. Before giving the l i s t , however, we would recall some general

facts about the functioning of the library. ALGOL-60 [ l ] and FORTRAN-

CERN [2] have been adopted as the official algorithmic languages. All

the programs at present in the library are written for the BESM-6 computer,

with the BESM-ALGOL (Computer Centre of the USSR Academy of Sciences) [3]

and ALGOL-GDR [4] translators being used for ALGOL problems and one

FORTRAN-DUBNA translator for FORTRAN problems. The two last-mentioned

translators form part of the "Dubna" monitor system [5] . Besides i ts

designation and the names of the authors, we give for each of the programs

below a brief description and certain cataloguing data, including:

1. The program cipher, consisting of three let ters and three digits .

The first two let ters of the cipher indicate the subject-matter

of the problem to be solved, while the third le t ter indicates

the language in which the program is written; the three digits

constitute a serial number. The subject breakdown is as follows:

AP - atomic physics; NP - nuclear physics; QM - quantum mechanics;

CT - the purely mathematical methods used most often in physics

calculations;

2. The language in which the program is written;

3. The translator for which the program is designed;

4. The program scope. When the FORTRAN-DUBNA and ALGOL-GDR

translators are used, the program scope is determined on the

basis of the loading instructions [5] - i . e . with allowance for

all duty sub-programs of the "Dubna" monitor system. When the

BESM-ALGOL translator is used, the program scope is indicated

without allowance for duty sub-programs;

- 22 -

5. A desc r ip t ion of the program - i . e . the l i t e r a t u r e source which

describes or wi l l describe the formulation of the problem, the

method of solving i t , the s t ruc tu re of the program, the ru les for

data input and the p r in t -ou t t e x t .

All programs in the Data Centre*s l i b r a r y can be supplied on request

in the form of a l i s t i n g and a se t of punched cards .

REFERENCES

[ l ] The algori thmic language ALGOL-6O, revised report ( in Russian), Mir,

Moscow (1965).

[ 2 ] The FORTRAN language ( in Russian), edi ted by SHIRIKOV, V.P. , Dubna

(1970).

[ 3 ] KUROCHKIN, V.M. et a l . , The BESM-6-ALGOL system ( in Russian),

Computer Centre of Moscow S ta te Univers i ty , Moscow (1969).

[4 ] HIRR, R., STROBEL, R., ALGOL in the "Dubna" monitor system ( in Russian) ,

t r a n s l a t e d from German by B.P. Primochkin, 1.7. Kurchatov I n s t i t u t e of

Atomic Energy, Moscow (1972).

[ 5 ] MAZNY, G.L., Guide for working with the "Dubna" monitor system ( in

Russian) , Jo in t Nuclear Research I n s t i t u t e , Dubna (1972).

- 23 -

I . A T O M I C P H Y S I C S

The "ATOM" system of mathematical a ids for atomic c a l c u l a t i o n s

I . PROGRAM FOR SOLVING HARTREE-FOCK SELF-CONSISTENT FIELD EQUATIONS FOR ATOMS

Cipher: APAOO1

Language: ALGOL-6O

Translator: BESM-ALGOL

Program scope: lOHOn ce l l s

Descr ipt ion: L.V. Chernysheva, N.A. Cherepkov, V. Radoevich

Preprint FTI-486, Leningrad (1975)

The program ca lcu la tes wave functions of the ground s t a t e of an atom or

ion in the Hartree-Fock n o n - r e l a t i v i s t i c approximation. The system of se l f -

consis tent equations is solved by the method of successive refinements of

funct ions . The so lu t ion i s sought in the form of one S l a t e r determinant or

a l i n e a r combination of severa l determinants corresponding t o a ce r t a in

configuration and term.

The "ATOM" system of mathematical aids for atomic ca lcu la t ions

II. PROGRAM FOR CALCULATING THE HARTREE-FOCK WAVE FUNCTIONS OF DISCRETEAND CONTINUOUS SPECTRA IN THE FIELD OF A "FROZEN" ATOMIC CORE

C i p h e r : APA002

L a n g u a g e : ALGOL-60


Program scope: 13001g c e l l s

Descr ip t ion: L.V. Chernysheva, N. Cherepkov, V. Radoevich

Preprint FTI-487, Leningrad (1975)

The program ca lcu la tes Hartree-Fock exci ted e lec t ron wave functions of

d i sc re t e or continuous spec t ra in the f i e ld of a "frozen" atomic core -

i . e . without se l f -cons i s tency with the functions of the occupied s t a t e s .

The core + e lec t ron system can be character ized by a term or merely by the

values of the project ions of o r b i t a l moments and spins of e l e c t r o n s . The

wave functions thus found are orthogonal t o the occupied s t a t e s . The

phase i s ca lcu la ted for functions of the continuous spectrum.

- 24 -

The'&TOM" system of mathematical aids for atomic calculations

I I I . PROGRAM FOR CALCULATING GENERALIZED OSCILLATOR STRENGTHS OF ATOMS WITHWAVE FUNCTIONS IN THE HARTREE-FOCK APPROXIMATION AND WITH ALLOWANCE FORMULTI-ELECTRON CORRELATIONS IN ONE TRANSITION

C i p h e r : APAOO3

L a n g u a g e : ALGOL-6O

Translator: BE3M-ALG0L

Program scope: 15347o ce l l s

Description: L.V. Chernyshevaf M.Ya. Amusya, S . I . Sheftel

Preprint FT1-493, Leningrad (1975)

The program calculates generalized osc i l l a to r strengths of atoms with

wave functions in the Hartree-Fock approximation (s ingle-par t ic le calculation)

and with allowance for mult i-electron correlat ions in the approximation of

random phases with exchange. I t enables one t o take into account correlat ions

only within the framework of one t r a n s i t i o n .

The "ATOM11 system of mathematical aids for atomic calculations

IV. PROGRAM FOR CALCULATING GENERALIZED OSCILLATOR STRENGTHS OF ATOMSWITH ALLOWANCE FOR MULTI-ELECTRON CORRELATIONS IN TWO TRANSITIONS

C i p h e r : APAOO4

L a n g u a g e : ALGOL-60



Descr ip t ion: L.V. Chernysheva, M.Ya. Amusya, S . I . Sheftel

Preprint FT1-495, Leningrad (1975)

The program ca lcu la tes general ized o s c i l l a t o r s t rengths of atoms with

wave functions in the Hartree-Fock approximation ( s i n g l e - p a r t i c l e ca lcu la t ion)

and with allowance for mul t i -e lec t ron cor re la t ions in the approximation of

random phases with exchange. I t finds general ized o s c i l l a t o r s t rengths

with allowance for cor re la t ions in two t r a n s i t i o n s simultaneously.

The system of programs e n t i t l e d "The atom in the r e l a t i v i s t i c approximation.

THE INTERACTION OP GAMMA RADIATION AND OP THE NUCLEUS WITH THE ELECTRONS OPTHE ATOM"

Cipher : APFOO5-O12

Language: FORTRAN-CERN

Translator: PORTRAN-DUBNA

System scope : 400OOQ c e l l s

Description: I.M. Band, M.B. Trzhaskovskaya, M.A. Listengarten

(in press)

The proposed system of programs is designed for studying atomic structures

by the Hartree-Pock method in the relativist ic approximation and for investi-

gating the processes involved in the interaction of gamma radiation and of

the nucleus with the electrons of the atomic shell. At present, the system

comprises the following programs:

APPOO55 Program for calculating the self-consistency of a field of an

atom in accordance with Hartree-Pock with stat is t ical allowance for

exchange in accordance with Slater in the (HPSD) relativistic approxi-

mation;

APPOO6: Program for making the field of an atom self-consistent in

the condensed state with boundary conditions of the Wigner-Seitz type

in the (HFSD) approximation;

APPOO7: Calculation of radial wave functions of an electron in a

discrete spectrum for any set of arguments;

APFOO8: Calculation of radial wave functions of an electron with

boundary conditions of the Wigner-Seitz type for any set of arguments;

APPOO91 Calculation of radial wave functions of an electron in a

continuous spectrum with definite orbital and total angular moments

for any set of arguments;

APPO1O: Calculation of amplitudes at zero and phase differences at

infinity of wave functions of continuous-spectrum electrons in the

self-consistent field of an atom;

APPO11: Calculation of coefficients of internal conversion of gamma

radiation and of conversion matrix elements in any atomic shell with

the Mno penetration" and "surface currents11 models;

- 26 -

APP012: Calculation of photo-effect cross-sections in the relativistic

cross-section in any atomic shell.

Within the above range of problems the system of programs will be added

to and expanded. Beside the programs enumerated, each of which has an

independent field of application, the system includes a number of duty

programs. The system is a closedone- i .e . it does not require the use of

programs not forming part of i t .

- 27 -

I I . N U C L E A R P H Y S I C S

PROGRAM FOR CALCULATING PAIR MATRIX ELEMENTS FOR VELOCITY-INDEPENDENTNUCLEAR FORCES AND THE COULOMB INTERACTION IN A SPHERICALLY SYMMETRICOSCILLATOR BASE ( j j COUPLING SCHEME)

C i p h e r : NPAOO1

Language : ALGOL-60

Translator: ALGOL-GDR


Descr ip t ion: V . I . Isakov, Yu . I . Kharitonov

Preprint LIYaF-47, Leningrad (1973)

The program ca lcu la tes p a i r matrix elements of Wigner, s i n g l e t ,

t enso r and Coulomb forces . The base cons is t s of two-par t i c le wave vectors

with a de f in i t e t o t a l angular momentum which are derived from s i n g l e -

p a r t i c l e wave functions of a sphe r i ca l ly symmetric harmonic o s c i l l a t o r in

accordance with the j j coupling scheme. The r ad i a l dependence of the

forces can be in the form e i t h e r of a 6-function or of a Gaussian wel l ;

in the latter case, there is provision for changing the interaction radius.

The program enables one to calculate pair matrix elements for any single-

particle states within the limits of the shell model. The Pauli principle

is not taken into account in the variant of the program.

PROGRAM FOR CALCULATING ANTISYMMETRIC PAIR MATRIX ELEMENTS FOR TELOCITY-INDEPENDENT NUCLEAR FORCES AND THE COULOMB INTERACTION IN' A SPHERICALLYSYMMETRIC OSCILLATOR BASE ( j j COUPLING SCHEME)

Cipher: NPA002

Language: ALGOL-60

T rans la t or : ALGOL-GDR



Prepr int LIYaF-47» Leningrad (1973)

This program i s a var ian t of program NPA001, in which the same matrix

elements are ca lcu la ted with respect t o antisymmetric two-par t i c l e wave

funct ions .

- 28 -

PROGRAM FOR CALCULATING PAIR MATRIX ELEMENTS OF CENTRAL FORCES WITH SDJGLE-PARTICLE WAVE FUNCTIONS IN SAXON-WOODS POTENTIALS AND A HARMONIC OSCILLATOR

C i p h e r : NPFOO3

Language : FORTRAN-CERN

Translator: FORTRAN-DUBNA

Program scope: 2621On c e l l s

Descript ion: S.A. Artamonov, Yu. I . Kharitonov


The f i r s t part of t h i s program solves the s i n g l e - p a r t i c l e Schr*<3dinger

equation with a Saxon-Woods po ten t i a l f in which sp in-orb i t i n t e rac t ion and

Coulomb po ten t ia l are a l so taken in to account. With the help of the s i n g l e -

p a r t i c l e wave functions obtained, the second part of the program constructs

two-par t ic le wave functions with a def in i t e t o t a l angular momentum and ca l -

culates pa i r matrix elements of Wigner, sp in-sp in , s i n g l e t , t r i p l e t and

Coulomb forces . The rad ia l dependence of the forces can be in the form of

a Gauss or a Yukawa p o t e n t i a l , for which the act ion radius can be changed,

and a l so in the form of a o-funct ion. For a given set of s i n g l e - p a r t i c l e

quantum numbers the matrix elements are calcula ted e i t h e r for a given value

of the t o t a l angular momentum or for a l l i t s possible va lues .

PROGRAM FOR CALCULATING PAIR MATRIX ELEMENTS OF THE n-p INTERACTION PRODUCEDBY CENTRAL FORCES IN DEFORMED ODD-ODD NUCLEI

Cipher: NPA004

Language: ALGOL-60


Program scope: 12406g ce l l s

Descr ipt ion: I . S . Guseva, Yu . I . Kharitonov


The program ca lcu la tes p a i r matrix elements of Wigner and sp in-sp in

forces . Functions describing the motion of a p a r t i c l e in a Nilsson

po ten t i a l are used as s i n g l e - p a r t i c l e wave funct ions. The rad ia l dependence

of the forces can be in the form e i t h e r of a Gaussian wel l , for which the

act ion radius can be changed, or of a 6-funct ion. For the program t o

function, one must introduce as numerical mater ia l the expansion coeff ic ien ts

of a s i n g l e - p a r t i c l e wave function in a deformed po ten t i a l with respect t o

wave functions of a sphe r i ca l ly symmetric harmonic p o t e n t i a l .

- 29 -

THE "DEPTH" PROGRAM FOR DETERMINING THE DEPTH OP A SPHERICALLY SYMMETRICPOTENTIAL FOR THE WAVE FUNCTION OF A NEUTRON WITH GIVEN QPANTUM NUMBERS

C i p h e r : NPFOO5



Program scope: 135Q4o c e l l s

Descr ipt ion: S.G. Ogloblin

Preprint LIYaF-ll8, Leningrad (1974)

The "DEPTH" program determines the depth of a sphe r i ca l ly symmetric

Saxon-Woods po ten t i a l at which a neutron - in a ce r t a in d i s c r e t e s t a t e or

near a s i n g l e - p a r t i c l e resonance - has a given energy E. For a d i sc re t e

spectrum, the s t a t e of the neutron is defined "by specifying the main quantum

number N, the o rb i t a l angular momentum I and the t o t a l angular momentum j .

For a continuous spectrum, near the s i n g l e - p a r t i c l e resonance the s t a t e of

the neutron is a l so defined by, in addi t ion t o the above quantum numbers,

the s c a t t e r i n g phase b - (45° - &» - - 135°)• Besides tne po t en t i a l well

depth, the program gives values of the r ad ia l wave function as a function

of the rad ius .

PAIR MATRIX ELEMENTS OF A TWO-PARTICLE SPIN-ORBIT INTERACTION IN ASFHERICALLY SYMMETRIC OSCILLATOR BASE ( j j COUPLING SCHEME)

Cipher: NPAOO6

Language: ALGOL-60


Program scope: 1225Og ce l l s



The program ca lcu la tes p a i r matrix elements of a two-par t i c l e sp in -

orbi t i n t e r a c t i o n . The base i s comprised of two-par t i c l e wave functions

with a ce r t a in t o t a l angular momentum derived from s i n g l e - p a r t i c l e wave

functions of a sphe r i ca l ly symmetric harmonic o s c i l l a t o r in accordance

with the j j coupling scheme. The r ad ia l dependence of the forces i s in

the form of a Gaussian well with a va r i ab le ac t ion r ad ius . The program

enables one t o ca lcu la te matrix elements both between non-symmetrized wave

functions (neutron-proton in t e rac t ion ) and between antisymmetric wave

- 30 -

functions ( i den t i ca l nucleons) . In both cases , the matrix elements can be

calcula ted e i t h e r for one specif ied value of the t o t a l momentum J or for

a l l i t s possible va lues . With t h i s var ian t of the program one can use

s i n g l e - p a r t i c l e wave functions with a pr inc ipa l o s c i l l a t o r quantum number

N = 2n + 1 ^ 7 .

RADIAL INTEGRALS OP A PAIR INTERACTION FOR GAUSS, DELTA-SHAPED AND COULOMBPOTENTIALS IN AN OSCILLATOR BASE

Cipher: NPA007

Language: ALGOL-60


Program scope: 10305o c e l l s

Descr ipt ion: V . I . Isakov, Yu . I . Kharitonov, I.V. Nik i t ina

(in press)

The program calculates pair radial integrals for Gauss, delta-shaped

and Coulomb potentials in a spherically symmetric oscillator base. For

specified single-particle quantum numbers of the four wave functions, the

radial integrals are calculated for all possible ranks, which are resolved

by the selection rules attributable to the angular parts of the corresponding

total matrix elements of the residual interaction. With this program, which

is based on program NPA001, one can use single-particle radial functions

relating to states with the principal oscillator quantum number N = 2n + 1 <• 7.

PROBABILITIES OP ELECTROMAGNETIC TRANSITIONS IN ODD DEFORMED NUCLEI

C i p h e r : NPA008

Language: ALGOL-60


Program scope: 15000g cells

Description: I.S. Guseva, Yu.I. Kharitonov (in press)

The type and multipolarity (xL) of the most intense gamma transitions

(not more than two) are determined on the basis of specified characteristics

of the initial and final states of an odd deformed nucleus. On the basis

of the Nilsson model, the reduced probabilities B(xL), the probabilities W(xL)

and the partial half-lives Ti are calculated for these electromagnetic

transitions. The wave functions of the initial and final states are found

by means of a sub-program which solves the Schrttdinger equation with a

Nilsson potential and which is one of the procedures making up the program.

- 31 -

Consequently, as characteristics of the initial and final states it is

enough to specify the level spins, their projections onto the symmetry

axis of the nucleus and the asymptotic quantum numbers of the corresponding

Nilsson orbitals. Provision is made for varying the deformation parameter

and other parameters of the potential.

PROBABILITIES OF ELECTROMAGNETIC TRANSITIONS IN ODD-ODD DEFORMED NUCLEI

C i p h e r : NPAOO9

Language : ALGOL-6O


Program scope: 16334a c e l l s

Descr ip t ion: I . S . Guseva ( in press)

The type and mul t ipo la r i ty (xL) of the most intense t r a n s i t i o n s (not

more than two) are determined on the bas i s of speci f ied c h a r a c t e r i s t i c s

of the i n i t i a l and f ina l s t a t e s of an odd-odd deformed nucleus . The

reduced p r o b a b i l i t i e s B(xL), the p r o b a b i l i t i e s W(xL) and p a r t i a l h a l f - l i v e s

T_ are ca lcu la ted for these electromagnetic t r a n s i t i o n s . The s i n g l e -2

p a r t i c l e wave functions of the neutron and proton are ca lcula ted by means

of a sub-program which solves the Schr*<3dinger equation with a Nilsson

po ten t i a l and which i s one of the procedures making up the program. All

possible neutron and proton wave function coupling schemes are considered.

Provision is made for varying the deformation parameter and other parameters

of the Nilsson p o t e n t i a l .

PAIR MATRIX ELEMENTS OF A TWO-PARTICLE SPIN-ORBIT NEUTRON-PROTON INTERACTION(OSCILLATOR BASE)

Cipher: NPAO1O

Language: ALGOL-6O




The program ca lcu la tes p a i r matrix elements of a two-par t ic le sp in -o rb i t

i n t e r a c t i o n . The base is comprised of two-par t i c le wave functions with a

ce r t a in t o t a l angular momentum derived from s i n g l e - p a r t i c l e wave functions

of a sphe r i ca l ly symmetric harmonic o s c i l l a t o r in accordance with the j j

coupling scheme. The rad ia l dependence of the forces i s in the form of a

Gaussian well with a var iab le ac t ion r ad iu s . The method of ca l cu la t ing

p a i r matrix elements i s based on the use of Talmi-Moshinsky coe f f i c i en t s ,

- 32 -

which enable one t o i so l a t e in a two-par t ic le wave function the movement

of the centre of gravi ty and the r e l a t i ve motion. This program duplicates

program NPAOO6. Hence, the two programs, which ca lcula te the same matrix

elements but by completely dif ferent methods, can be used for mutual

v e r i f i c a t i o n of the correctness of the calcula t ions performed.

THE "DISF1 PROGRAM FOR CALCULATING THE DISCRETE SPECTRUM OF THE INTRINSICENERGIES AND EIGENWAVE FUNCTIONS OF A SINGLE-PARTICLE SCHR*O"DINGER ELATIONWITH A SPHERICAL POTENTIAL OF FINITE DEPTH

Cipher: NPF011

Language: FORT RAN-CERN



Description: L.P. Lapina (in press)

The "DISF1 program solves a radial Schr*<5dinger equation with a Saxon-

Woods potential in which Batty-Greenlees parametrization (Nuclear Physics A 13:

(1969) 673) is used. The possibility is provided of solving this equation

for any other spherically symmetric potential of finite depth. With the

"DISF1 program it is possible to obtain the whole discrete spectrum of

energies, calculate the energies of several levels for specified initial

approximations and determine the radial wave function and its derivative

with respect to the argument at a specified energy for one level.

THE "ME2P1H11 PROGRAM FOR CALCULATING MATRIX ELEMENTS OF A RESIDUAL INTER-ACTION FOR STATES OF THE TYPE 2 p - l h (CENTRAL FORCES)

C i p h e r : NPF012

L a n g u a g e : FORTRAN-CERN


Program scope: 4 5 7 1 6 Q c e l l s

Description: S.A. Artamonov, S.G. Ogloblin (in press)

The "ME2PlHn program is designed for calculating, in spherical nuclei,

matrix elements of a residual nucleon-nucleon interaction produced by

Wigner and singlet forces for states of the type 2p-lh. The radial

dependence of the forces can be in the form either of a &-potential or of

Gauss or Yukawa potentials. Single-particle wave functions axe calculated

in a Saxon-Woods potential. The wave functions of states of the type 2p-lh

are constructed as follows: first the angular momenta of the particles

are added, the resulting momentum then being added together with the

angular momentum of the hole to the total spin of the state under considera-

tion. There is provision for the transfer of the calculated matrix elements

- 33 -

t o e x t e r n a l s t o r a g e (magnetic t a p e , drum, d i s k , punched ca rds ) for

f u r t h e r p r o c e s s i n g .

EIGENVALUES AND EIGENFUNCTIONS OP A SINGLE-PARTICLE MODEL OP A NUCLEUSWITH A FINITE DEFORMED POTENTIAL HAVING A BLURRED EDGE; SPECIFICATIONOF THE SHAPE OF THE NUCLEAR SURFACE IN THE LEMNISCATE SYSTEM OF CO-ORDINATES

Cipher : NPPO13

Language: FORTRAN-CERN


Program scope : 35633o c e l l s

Description: V.V. Pashkevich, V.A. Rubchenya (in press)

The program is designed for calculating the single-particle spectrum

and eigenvectors of single-particle states in a nuclear potential of finite

depth with a blurred edge. The shape of the nucleus is specified in

lemniscate co-ordinates. This enables one to perform calculations for

axially symmetric nuclei, the shape of which may vary from oblate to

separation of the nucleus into two fragments. The eigenvalue problem is

solved by the diagonalization method. Functions of a deformed, axially

symmetric, oscillator potential are used as the base set of functions.

- 34 -

I I I . Q U A N T U M M E C H A N I C S

PROGRAM FOR CALCULATING CLEBSCH-GORDAN COEFFICIENTS WITH ZERO MAGNETICQUANTUM NUMBERS

C i p h e r : C84AOO1, QMFOO1

Language : ALGOL-6O, FORTRAN-CERN

Translator: ALGOL-GDR, FORTRAN-DUBNA

Program scope: ^ 3 5 Q sn^- 66O2Q c e l l s r e spec t i ve ly

Descr ip t ion : S.A. Artamonov, V . I , Isakov, Y u . I . Kharitonov

Prepr in t LJYaF-73, Leningrad (1973)

These programs enable one t o ca l cu la t e the values of indiv idual Clebsch-

Gordan coef f i c i en t s with zero magnetic quantum numbers provided t h a t t he

ar i thme t i c sum of the angular momenta under cons idera t ion does not exceed

4 3 . P r in t -ou t both of the i n i t i a l parameters and of the computational

r e s u l t s in t a b u l a r form i s provided fo r . The procedures (sub-programs)

making up these programs can be used as ready blocks when programming the

more complex problems which conta in such coe f f i c i en t s as component p a r t s .

PROGRAMS FOR CALCULATING CLEBSCH-GORDAN COEFFICIENTS OF A GENERAL FORM

Cipher: QMAOO2, QMFOO2



Program scope: 7l67o an^L 7133o c e l l s r e spec t ive ly

Descr ip t ion: S.A. Artamonov, V . I , Isakov, Yu . I . Kharitonov

Prepr in t LIYaF-73, Leningrad (1973)

The programs enable one t o ca lcu la t e values of individual Clebsch-

Gordan coef f ic ien ts for spec i f ied values of th ree angular momenta and a l so

t h e i r projec t ions provided tha t the a r i thmet ic sum of the angular momenta

under considerat ion does not exceed 4 3 . Pr in t -out both of the i n i t i a l

parameters and of the computational r e s u l t s in t a b u l a r form i s provided

for . The procedures (sub-programs) making up these programs can be used

as ready blocks when programming the more complex problems, which contain

Clebsch-Gordan coef f i c ien t s of a general form as component p a r t s .

- 35 -

PROGRAMS FOR CALCULATIHG RACAH COEFFICIENTS

C i p h e r : <$IAOO3, QMFOO3



Program scope: 7OO5Q and 7H3o c e l l s r e s p e c t i v e l y

Description: V.N. Guman, S.A. Artamonov, Yu.I. Kharitonov

Preprint LHaF-76, Leningrad (1973)

These programs enable one to calculate the values of individual Racah

coefficients provided that the factorals nj encountered in the calculations

are limited by the quantity nj = 44. This range of variations of the para-

meters is quite sufficient for most spectroscopic calculations. Print-out

of the init ial parameters and of the computational results in tabular form

is provided for. The procedures (sub-programs) making up these programs

can be used in solving those problems which contain Racah coefficients as

component parts.

PROGRAMS FOR CALCULATING 9J-SYMBOLS

C i p h e r : <$1AOO4, QMFOO4


Translator: ALGOL-GDR, FORTRAHT-DUBNA

Program scope : 716OQ and 7364o c e l l s r e s p e c t i v e l y

Description: S.A. Artamonov, Yu.I. Kharitonov

Preprint LIYaF-ll6, Leningrad (1974)

The program enables one to calculate individual values of 9j—symbols

provided that the arithmetic sum of the angular momenta in any of the six

triads does not exceed 43; this is quite sufficient for most spectroscopic

calculations. Print-out of the init ial parameters and of the computational

results in tabular form is provided for. The procedures (sub-programs)

making up these programs can be used in solving those problems which contain

93-symbols as component parts. There is some limitation to the program for

calculating 9j-synibols which forms part of the ALGOL program whose text is

presented in Preprint LIYaF-116. In the Comment on the program for

calculating 93-symbols published in the present Bulletin, this question is

considered in detail and the text of the corrected procedure is presented.

- 36 -

PROGRAM FOR CALCULATING d ^ i f a ) WIGNER FUNCTIONS

Cipher:

Language: ALGOL-6O


Program scope: ^435o c e l l s

Descr ipt ion: I . S . Guseva

Preprint LHaF-124, Leningrad (1974)

The program ca lcu la tes cL^,, (fl) Wigner functions with given quantum

numbers I, M and Mf and angle & varying through 5° intervals from 0° to 90°»

Quantum numbers I, M and Mf can assume whole and semi-whole values. For

angles greater than 90°t d-function values are easy to obtain by using the

appropriate relation presented in the preprint. Print-out of the ini t ial

parameters and of the computational results in tabular form is provided for.

THE "CFP1A" PROGRAM FOR CALCULATING GENEALOGIC COEFFICIENTS OF SEPARATIONOF A SINGLE PARTICLE FOR ANTISYMMETRIC STATES OF IDENTICAL FERMI0H5( j j COUPLING SCHEME)

C i p h e r : Qp£F006


Translator: FORTRAN-BUBNA


Description: S.A. Artamonov, Yu.I. Kharitonov ( in press)

The "CFP1A" program calculates genealogic coefficients of separation

of a single par t i c le (GCl) from antisymmetric s ta tes Ij saJM> constructed

in accordance with the j j coupling scheme and belonging to configurations

of the type j j n j . For angular momenta j = 5/2, 7/2, 9/2 and l l / 2 , the

GCls are calculated with a number of par t i c les n ranging from 3 t o

j + l / 2 for j = 13/2 with n = 3, 4 and for j = 15/2 only for th ree -par t i c le

s t a t e s . At the same time, the GCls are calculated for a l l possible values

of the to t a l angular momentum J , of the senior i ty quantum number s and the

additional quantum number a. The GCls can be calculated e i ther for the

whole parameter var ia t ion range indicated above or for any part of i t .

Print-out of the computational resul t s in the form of tables s imilar to

those of Bayman and Lande (Nuclear Physics 21 (*966) l ) is provided for,

as is external storage of the resul ts (on magnetic tape, drum, disk, punched

cards) . The GCls are calculated by diagonalizing matrices of Casimir

operators of a special unitary and a symplectic group.

- 37 -

THE "CFP1B" PROGRAM FOR CALCULATING GENEALOGIC COEFFICIENTS OF SEPARATIONOF A SINGLE PARTICLE FOR ANTISYMMETRIC STATES OF IDENTICAL FERMIONS( j j COUPLING SCHEME) IN QUANTUM-MECHANICAL COMPUTATIONS

C i p h e r : GfltFOO7


T r a n s 1 a t o r : FORTRAN-DUBNA

Program s c o p e : 10763o c e l l s

Descript ion: S.A. Artamonov, Yu. I . Kharitonov ( in press)

The "CFPIB" program i s designed for use as a sub-program in the case

of quantum-mechanical problems where i t is necessary t o ca lcu la te various

quant i t i e s which include a GC1. The range of v a r i a t i o n of the parameters

for which GCls can be calcula ted i s the same as in the case of program

"CFPIA" (see above). Program "CFP1B" i s used for economizing on in te rna l

memory, i t t r ans fe r s the GCls calculated by program "CFP1A" from external

storage (magnetic t ape , drum, disk, punched cards) in to the in te rna l

memory. The t r a n s f e r i s effected on the bas i s of specif ied parameters

which uniquely determine the desired set of GCls. The p a r a l l e l p r in t -out

of GCls in t abu la r form i s provided for .

PROGRAM FOR CALCULATING CLEBSCH-GORDAN COEFFICIENTS IN SIMPLE FRACTIONS

Cipher: GJ5AOO8

Language: ALGOL-60


Program scope: 23462r> ce l l s

Descr ipt ion: T.V. Alenicheva ( in press)

The program enables one t o ca lcu la te Clebsch-Gordan coeff ic ients in

the form (a/b)Yc/d, where a i s a whole number (with a s i g n ) , b , c and d

are na tura l numbers, and a/b and c/d are i r reduc ib le f r ac t i ons . The

form (a/b)^c/d is a general one; i f the value obtained for the Clebsch-

Gordan coeff ic ients has an a r i thmet i ca l ly simpler form, the corresponding

simplif ied expression i s pr in ted out . Clebsch-Gordan coeff ic ients in a

form which i s convenient for t h e o r e t i c a l ca lcula t ions by hand should i f

possible be used before they become cumbersome. This l imi t s the range

of va r i a t i on of the i n i t i a l parameters and thus determines the p o s s i b i l i t i e s

of the program. The present program enables one t o ca lcula te Clebsch-Gordan

coeff ic ients in the form indicated as long as the ar i thmet ic sum of the

- 38 -

three momenta under consideration does not exceed 36. The values of

the initial parameters and the computational results are printed out in

the form indicated and also in the form of a decimal fraction.

PROGRAM FOR CALCULATING RACAH COEFFICIENTS IN SIMPLE FRACTIOUS

Cipher: (3VLA.OO9

Language: ALGOL-6O



Descr ip t ion: T.V. Alenicheva ( in press)

The program enables one t o ca lcu la te individual Racah coef f ic ien ts in

the form (a/b)"y c/d, where a i s a whole number (with a s i g n ) , b , c and d

are na tu ra l numbers, and a/b and c/d are i r reduc ib le f r ac t i ons . The

program i s bes t used in cases where the ar i thmet ic sum of the angular momenta

in any of the four coeff ic ient t r i a d s does not exceed 36. With higher t r i a d

va lues , t he expressions for the Racah coeff ic ients become very cumbersome

and hence inconvenient for ca lcu la t ions by hand. The form of p r in t -ou t

of the i n i t i a l da ta and the computational r e s u l t s i s the same as in the

case of program QMAOO8.

TALMI-MOSHUJSKY TRANSFORMATION COEFFICIENTS

Cipher:

Language: ALGOL-60


Program scope: 103580 c e l l s


This program ca lcu la te s Talmi-Moshinsky transformation coe f f i c i en t s ,

which enable one t o go from a desc r ip t ion of the independent motion of two

p a r t i c l e s in the f i e l d of a three-dimensional sphe r i ca l ly symmetric harmonic

o s c i l l a t o r t o a desc r ip t ion of the movement of the centre of g rav i ty of these

particles and of their relative motion. Print-out of the initial parameters

and of the computational results in tabular form is provided for. The program

is based on a procedure-function which can be used in more complex calculations

involving Talmi-Moshinsky coefficients.

- 39 -

PROGRAMS FOR CALCULATING 12J-SYMB0LS OP THE FIRST AND SECOND KIND

Cipher: QIAO11, QMFO11

Language: ALGOL-6O, FORTRAN-CERN


Program scope: 10427o and 11023a c e l l s r e spec t ive ly

Descr ip t ion: B.F . Gerasimenko, V.K. Khersonsky ( in press)

These programs enable one t o ca lcu la te the values of individual

12j-symbols of both the f i r s t and the second kind provided t ha t the sum

of the elements in any of the eight t r i a d s which can "be constructed from

the parameters of a 12j-symbol does not exceed 4 8 . The same condi t ion

must be f u l f i l l e d for a minimum value of the doubled sums of pa i r s of

corresponding parameters of the upper and lower l i n e s in a 12j-symbol of

the f i r s t kind - or only of the lower l i n e for a 12j-symbol of the second

kind. Such a range of v a r i a t i o n of the parameters of 12j-symbols i s

qui te su f f i c i en t for most spectroscopic c a l c u l a t i o n s . The programs

can be used as sub-programs in solving problems which involve 12j-symbols.

P r in t -ou t of the i n i t i a l parameters and of the computational r e s u l t s in

t a b u l a r form i s provided fo r .

PROGRAM FOR CALCULATING ^ , ( 6 ) WIGNER FUNCTIONS

Cipher: QJIAO12

Language: ALGOL-6O

T rans1at or: ALGOL-GDR

Program scope: 7l6Og c e l l s

Descr ip t ion: I . S . Guseva


The program ca lcu la tes d ^ ^ U ) Wigner functions with given quantum

numbers I , M and M1 for any range of v a r i a t i o n of the angle & between 0°

and 90° with any given increment (or s t e p ) . Quantum numbers I , M and M1

can assume whole and semi-whole v a l u e s . P r in t -ou t of the i n i t i a l data

and computational r e s u l t s in t a b u l a r form is provided fo r .

- 40 -

TABLES OP ELECTRON ENERGY EIGENVALUES, DENSITIES NEARZERO AND MEAN VALUES IN SELF-CONSISTENT FIELDS

OF ATOMS AND IONS

I .M. Band , M.B. T r z h a s k o v s k a y a

The tables contain quantities calculated in self-consistent fields

of atoms and ions. Self-consistency was achieved in a relativistic variant

of the Hartree-Fock-Slater method with allowance for the finite dimensions

of the nucleus. The calculations were performed, "both with and without

Letter's correction, for many atoms and ions from helium to plutonium

(2 ^ Z ^ 94)» In the tables are presented electron energy eigenvalues,

the coefficients If associated with electron density <?(r) near zero

(N = N * 137.0388~'2"'-1\ where N = lim 4*Q(r)r~'2;j-1' for r - 0 ) and the

mean values of the potential energy and the degrees of the radius rn

(n = - 3» - 1» 1» 2) and also the total energy of the atom. Singly

charged positive and negative ions and multiply ionized atoms were con-

sidered. In individual cases, computational results are presented for

several different electron configurations of the same element.

The tables are published as LIYaF preprints:

for the elements 2 ^ Z ^ 52 - Preprint 90, 1974;

for the elements 53 - Z "S 63 - Preprint 91, 1974;

for the elements 64 - Z ^ 94 - Preprint 92, 1974.

UDK 539.144 - 41 -

COMMENT ON THE PROCEDURE FOR CALCULATING 9J-SYMBOLS

B.P . Gerasimenko, Y u . I . Kharitonov

Reference [ l ] contains the texts of programs for calculating 9J-symbols

written in ALGOL-6O and FORTRAN-IV. Practical use of these programs has

revealed certain limitations of the 9j-symbol calculation procedure forming

part of the ALGOL program; in this program, the 9j-symbols are calculated

as the sum of the products of three Racah coefficients, the summation index

being able in the general case to assume either whole or semi-whole values.

In the ALGOL text in Ref. [ l ] , on the other hand, the variant uses only

whole values of the summation index. Generally speaking, in those cases

where the summation index assumes semi-whole values the ini t ial 9j-symbol

may - by line or column transpositions - be reduced to a form corresponding

to whole values of the summation index. Let us consider, for example,

a 93-symbol whose j parameters are semi-whole and whose L parameters are

whole - i . e .

f i i I 1

Jt h "U

Here, t h e l i m i t s of v a r i a t i o n of summation index k a re determined by t h e

conditions

"MVX, K £ mva (2)

It follows that the index k assumes semi-whole values. On the basis of

symmetry properties, the 9J-symbol determined by formula (l) can be

written in the form

'»L J(3)

- 42 -

In this formula, summation index k.. determined by the conditions

VMX. (4)

assumes (as can be seen) whole-number va lues .

I t should be noted t h a t , when one uses the procedure of 9j-symbols

for ca lcu la t ing the coeff ic ients of transformation A[jj-4.SJ from the j j

coupling scheme t o the LS coupling scheme which are frequently encountered

in nuclear ca lcu la t ions , the index k assumes whole values and hence in

t h i s case the procedure described in Ref. [ l ] gives correct r e s u l t s . The

same applies t o 9j-symbols a l l of whose parameters assume whole va lues .

Having in mind the same general case, one should regard the summation

index k as a var iab le of the rea l type and hence introduce changes in to

the t ex t of the 9j-symbol procedure. The corrected t ex t of t h i s procedure,

in which the designations from Ref. [ l ] have been retained as far as

poss ib le , has the form

;lVALUE»A1B,CtD,B,F,G,H,Jj

•BEGIN*•IffiALlP,QtR,K,KM1S;

S:=0;

P : = I A B S ( A - J ) J Q : = A B S ( D - H ) ; H : = A B S ( B - P ) ;

K:=P; •II'"K<QITKEN'K:=Q; 'IF'K-^'THEN'Kz^R;

P:i=A+J;Q:=I»-H;R:=B+Fl-KH:=P;»IFllQWitTHEMtKMi=Q;

* FOP.»K: =K * STEP • 1 * UNTIL • KM • DO •

W(A,B,J,F,C,K);J9:=S

Otherwise the ALGOL program for calculating 9j~symbols presented in

Ref. [ l ] remains unchanged.

REFERENCE

[ l ] AHPAMOHOV. SoAes KHARTTONOT, Yu. I 4 , Preprint LIYaP-116, Leningrad (1974).

Documents

IN DCINTERNATIONAL NUCLEAR DATA COMMITTEEI.A. Kondurov, Yu.V. Sergeenkov When one is compiling a machine library of nuclear level schemes, the question of the format for presenting