2.B : 2.L Nuclear Physics A330 (1979) 443-451 ; © North-Holland Publiahinp Co., AmrtedanrNot to be reproduced by photoprlnt or microfilm wdthout written permlulon fYom the publlaher

ELECTROEXCITATION OF THE ISOMER IN '°3Rh

T. SAITO, Y. OHKUBO,A. SHINOHARA, R. ARAKAWA fand K. OTOZAIDepartment of Chemistry, Faculty ofScience, Osaka University, Toyonaka, Osaka 560, Japan

Received 18 August 1978(Revised 14 May 1979)

Abstract : Coulomb excitation by electrons was investigated on '°'Rh by the radioactivity measurementof the isomer, near the threshold. Cross sections for the excitation ofa 357 keV level in'°'Rh whichdecays to the 56 min isomeric state with a branching of0.062 ~ were measured at electron energiesof350-800 keV ; the obtained value is, e.g, 2.3 x 10 -3 ' cmZ for 800 keV electrons. The experimentalcross sections agree with the theoretical ones which have been calculated from an approximateformula of de Forest and Walecka based on the oscillating liquid drop model.

E NUCLEAR REACTION`°'Rh(e,e'),E=350-$OOkeV ;measureda(E).

1. Introductlon

Nuclear excitation by electron transition (NEET) has been claimed to be a possiblemechanism, as well as X-ray and Auger electron emission, which deexcites an atomicexcitation due to an inner shell vacancy'). The NEET implies that a nucleus has acertain probability of being raised to the higher energy levels by means of electro-magnetic interactions between the nucleus and the extranuclear electrons when thenuclear and the electronic transitions have a common multipolarity and approxi-mately equal transition energies. Some evidence for NEET was first given in ta90sby detecting the isomer after irradiation with electrons in the range 72-lOQ keV[refs . s, 3)] . Coulomb excitation by means of electrons, a possibly competitivemechanism for isomer production, was unable to be responsible for the thresholdenergy value and the amount ofthe isomer observed in the experiments. In the latter,the contribution of Coulomb excitation was estimated by using an approximateformula of de Forest and Walecka a) based on the oscillating liquid drop model, andit was shown that the excitation function calculated was about twenty times smallerthan the experimental one 3). In the lowest energy regiom it is of signilïcance to testthe applicability of this formula further by experiments, because there are almost noexperimental studies of Coulomb excitation performed, especially in the region wellbelow 1 MeV.

f Preaent address : College ofGeneral Education, Osaka University, Toyonaka, Osaka 560.443

444

T. SAITO et al.

1o3Rh is a suitable nuclide on which the total cross section for Coulomb excitationcan be studied by using the radioactivity measurement of the induced isomer, althoughthe information on the differential cross section is unobtainable. The 295 keV and357 keV levels in'°3Rh are strongly excited by Coulomb excitation ; moreover, onlythe latter level has a detectable branch decaying to the isomeric state which has anappropriate half-life for the residual radioactivity measurement. Furthermore, in1°3Rh the occurrence of the NEET process need not be taken into account, sinceio3Rh does not fulfill the NEET conditions at all. In this paper we report the resultsofaCoulombexcitation experiment on 1 oaRh with electrons in the range35000keV.The total cross section for the 357 keV level excitation was compared with thatcalculated by the formula of de Forest and Walecka.

2 .1 . BOMBARDMENT

2. Experimental procedure

A metallic Rh foil 25 ~m (31 mg ~ cm - Z) thick and 26 mm ~ in diameter wasbombarded in air with 35000 keV electrons from a rectified transformer typeelectron accelerator in the Osaka Laboratory of the Japan Atomic Energy ResearchInstitute (JAERI). The bombarding electron energy was calibrated with an accuracyof about 10 keV by comparing the energy dissipation distribution in cellulose tri-acetate (CTA) films with that obtained with a Van de Graaff electron accelerator s),whose energy was determined by measuring the range of electrons in A1 and thethreshold ofthe 9Bdy, n)BBe reaction 6). The calibration included the energy degrada-tion of electrons in a0.03 mm thick titanium exit window of the accelerator, and alsoin air with a distance of 8 cm through which the electron beam traversed to the target .The current was monitored by an amperemeter connected to a target mount whichwas cooled with circulating water.

In the bombarding current measurement, reductions in currents due to electronsscattered out in the backward direction were corrected by estimating the coefficientsfor backscattering of incident electrons and emission of secondary electrons . Thebombarding current, l, was obtained from the measured current, I~�, by the relation

I = he..l(1- ns-~ls - nT~1é~1T),

(1)

where t1s is the secondary emission coeRcient, ns is the backscattering coefficient ofelectrons for the Rh target, q., and nT are the transmission coefficients of electronsthrough the target in their forward and backward movements, respectively, and néis the saturation backscattering coelïïcient for the target mount consisting of a thick(5 mm)Cu plate. For all incident energies, nswas set to be 0.005, thevalue Fredericksonplaced as an upper limit from his careful measurement'), while the other coeffcientswere determined for each incident electron energy, E°. In estimating these coefficients,the assumption was made that electrons traversed the interface of Rh and Cu

445

perpendicularly, and the electrons distributed in energy were delegated by mono-energetic .electrons with the most probable energy. Since the Rh target used wasnot so thick as to give the saturation backscattering, ~e was determined relative tothe saturation value, gB(sat), according to an empirical expression of Koral andCohen 8). The gB(sat) was obtained from an empirical equation for the backscatteringcoefficient at saturation by Tabata et al . 9), and by the same equation ne wasestimatedfor electrons with an energy of Em = E° -dEm, where dEm is the most probableenergy loss of transmitted electrons through the target in their forward movementand was calculated after Landau's theory 1°). The transmission coeflïcients nr and nTwere estimated by an empirical equation of Tabata and Ito' 1) . Here the nT is forelectrons of energy Em = Em -dF,m, where dE~ is the most probable energy lossof backscattered electrons from Cu [ref. ` 2)] . Theobtained values for qB and grqsqTwere 0.317-0.0694 and 0.0131-0.173, respectively, at 35000 keV, and the sums ofthem were unable to come to nB(sat) . The corrected bombarding currents were, e.g.,145 pA/0.665 = 218 ~A at 350 keV and 296 ~A/0.753 = 393 ~A at 800 keV.The bombarding currents were also estimated from the total output currents of

the accelerator and the relative current density at the target site which was obtainedby measuring the spatial dose distribution with CTA dosimeters' 3) . These valueswere in agreement with the corrected ones given above.

2 .2 . MEASUREMENT OF RADIOACTIVITY

ioa~

After 2h bombardment the radioactivity induced in the target was measured witha windowless Q-gas flow GM counter, surrounded by peripheral anticounters, witha background of below 1 count/min. The obtained decay curves of target activitywere analysed by the least-squares fit of the 1°3mRh component (t.t = 56.12 min)and a constant background component with the aid of the CLSQ code 1° ) using anACOS computer, since this experiment was free from radioactivities other thani°3mRh. As an example fig . 1 shows the decay curve obtained at an electron energyof 800 keV.

Since the target was thicker than the ranges of conversion electrons from' o3mRh,typically 4.1 mg~ cm -2 for L~onversion electrons, inevitable ambiguity was intro-duced in determining the detection ~cient of the electrons by the GM counter.In order to obtain the absolute cross sections, X-ray counting was carried out witha photon detector in the case of 720 keV and 800 keV. The number of Ka X-raysemitted per disintegration of ' °3mRh is expected to be 0.067 t0.008 [ref. 1 °)]. Thedetector was a hyperpure Ge low-energy photon spectrometer with resolution of290 eV at 20 keV. The absolute effciency curve was cônstructed by using calibratedpoint-like sources of ~41Am and "Co supplied by TRC. The average solid eagleof the target disk subtended by the detector was evaluated by a Monte Carlomethod'6). The absolute efficiency of the photon detector wasthen determined witha relative error of 15 ~.

446

T. SAITO et a/ .

Ea_uWF

F

fJ

TIbE (h)

Fig. 1 . Typical decay curve of '°'mRh obtained with 800 keV electrons. The solid lines indicate theresult of a least-squares fit .

2.3 . CORRECTION OF RADIOACTIVITY INDUCEDBY BACKSCATTERED ELECTRONS

Backscattered electrons can also excite a target nucleus in their backward traverseifthey still have sufficient energies . This contribution has to be corrected in the presentcase, since the backscattering is not insignificant because of lower incident energiesand a thicker target . Bothe has measured the relative distributions in energy of thebackscattered electrons at 370 and 680 keV incident energy on Cu, Sn, and others ") .The energy distributions of electrons backscattered from Rh and Cu respectivelyat incident energies of Eo = 35000 keV and E~, = Eo -dEm = 320-775 keV wereevaluated by interpolating and extrapolating Bothe's results linearly in incidentelectron energy and target atomic number. Here the assumption was made that theenergy distribution was not angular dependent and, in the case of Cu, it was givenfor the representative electrons with the most probable energyEm. The backscatteringcoefficients used here were those given for eq . (1). From the distributions obtainedin this manner, together with the ne, and ns, and the measured isomer yield curvewhich was used as the first preliminary excitation function, the true excitation funo-tion for isomer production was extracted by successive approximation. The largestcorrection was a reduction of the isomer yield by 9.1 ~ at 800 keV.

1~5

0_m0 0~5

d lso "

B d~

B = 6~2 x 10_4

3. Results and discussion

Fig. 2 shows the cross section for isomer production, ~,,o . Bars attached to eachpoint mean only the standard deviations in the radioactivity measurement, since wewere unable to estimate uncertainties in the measurement of the bombarding current,and in the correction applied to the radioactivity induced by backscattered electrons.We believe that the uncertainty in Qi,o is less than 30 ~.The level scheme of 1° 3Rh is shown in fig . 3 [refs . ta .'9)]. The i- level lying at

295 keVand the i_ level at 357 keVare a ono-phonon doublet in the oscillating liquiddrop model. Since B(E2)T values for these two levels are substantially equal, 0.22and0.37 in units of 10 -48 eZ ~ cm4 [ref. t e)], the cross sections for Coulomb excitationofthose levels may be considered to be the same order ofmagnitude . From the resultsof y-ray measurement of t°'Pd by Maclas et a(.' 9) with the at,a values compiledby Kocher t 8 ), one obtains an upper limit of 2.8 x 10- s for the branching ratio ofthe 295 keV level to the 40 keV isomeric state, B', and 6.2 x 10-4 for that of the 357keV level, B, namely, B/B' > 22 . Therefore, we can neglect the isomer production

E (ksV)

2~5

~0~5

]00200 300 400 500 600 700 800 900

N

û

Fig . 2 . Cross sections for isomer production in `°'Rh, a,� , in a functia~ of incident dectron energy,E . Cross sections for the 357 reV level excitation, oc, are also shown by the right ordinate. The solidline shows a theoretical excitation function calculated by e9. (2) with semi-empirical parameters, and

the dashed' line indicates that obtained with the experimental B(F-2)f values .

448

T. SALTO et al .

(7l2) 3J2.2.

512"

5/2-

3l2-

912.

rh~"~O

_~~.\

'°sRh

.,8yo

~(1~-

0)

~94 Z

k~ {~6z(21+ 1)

BtCt~!r(9a)~Z~

652 s5a608

537

712.112-

357

295

93

40 tiB,t2m1n

Fig. 3 . Level scheme of°'Rh below 800 keV. The double arrows indicate Coulomb excitation ; and thearrows with solid lines and with dashed lines indicate seen and unseen transitions in radioactive decay

studies, respectively . Transitions from the positive-parity quadruplets at 53752 keV are omitted .

through the 295 keV level, which is confirmed in our result obtained at 350 keV asshown in fig . 2. In addition, we can neglect theoretically the direct excitation of theisomeric state and the indirect one via a 93 keV level which decays to the isomericstate with a 100 ~ branching . From the reasons presented above, the excitationfunction for isomer production can be regarded to be proportional only to that forCoulomb excitation of the 357 keV level, Qc ; that is, Q;,° = BQ~. The value of Qcis given at the right ordinate in fig . 2.The experimental cross sections acwerecompared with thetheoretical values which

were calculated by a formula of de Forest and Walecka employing the oscillatingliquid drop model 4). The formula is given in the first Born approximation, and issimplified under the conditions that in the long wavelength limit the transverseelectric mpltipole matrix elements are reduced to be proportional to the longitudinalelectrostatic multipole matrix elements, and the transverse magnetic multipolematrix elements are equal to zero from parity considerations of the nuclear modelemployed. The differential cross section for one-surfon transition is then given asfollows [in rationalized natural units]

q

l

1+(k~-kt cos9)~E~'

(2)

where

Here B is the scattering angle ofelectrons, q and q~ are the three- and four-momentumtransfers, respectively, k, and k2 are the initial and final electron wave numbers,respectively,Qisgiven as Q = ?{k1 +k Z), w is the energy loss ofelectrons, cu = s, - eZ,

a istheméan radius oftheliquid drop nucleus, E' is the finaltotal energy ofthe nucleus,and the other symbols are used according to their conventional definitions. In thecase of 1 = 2, de Forest and Walecka have given the form factor as ~j Z(ga)IZ =(qa)4/(5 ! !) Z in the asymptotic form, and the transition probability as ZZ/( BZCZ)_ZZ x 3.24A - ' ie from the semi-empirical mass formula4).The differential cross sectionof the 357 keV level was calculated by inserting these relations into aq . (2). The totalcross section was obtained by summing the dit%rential over B numerically. Thecontribution of the longitudinal component is about 85 ~ in the whole range. Thetheoretical excitation function of the 357 keV. level is shown by the solid line in fig . 2.The agreement between the experimental values and the theoretical ones obtainedby following the treatment of de Forest and Walecka is on the whole good .The product of the mass parameter BZ and the restoring force parameter CZ can

be determined from the reduced E2 transition probability B(E2)j as

_ 3 Z

BZCZ

Zfi (4nZeRZ~ B(E2)j -1 .

(3)

The B(E2)j value has been given experimentally as ~B(E2)j =0.37 x 10-as eZ ~cm~ inthis case [ref.'8)] . We also calculated the cross sections for Coulomb excitation of the357 keV level by putting this value into eqs.(3) and (2) . In the calculation, the contribu-tion of the transverse magnetic component was neglected, because the mixing ratioS(E2/M1) is considered to be infinitely large and therefore onemay put B(M1)j = 0.The result is represented by the dashed line in fig. 2, and found to be about half theexperim~tal cross sections .Theisomer can also be induced through the 357 keV level by the resonance absorp-

tion of breansstrahlung radiations produced in the target. Thedumber bfthe isomeractivated per second by this process is given, by integrating the Breit-Wigner singlelevel formula, as

whereNx is thenumber oftarget nuclei per cmZ, ~the incident rate ofbremsstrahlung

450

T. SA1T0 el al.

radiations at resonance, ~ . the wavelength of resonant photon, g the statistical factorand !'o the partial width for the 357 keV radiative transitions. The observed B(E2)Tvalue leads to l'o = 5.7 geV. Energy spectra of bremsstrahlung radiations producedin the target by incident electrons of 350-500 keV were obtained from the tabulatedvalues z°) . The numbers of the isomer produced by this process were estimated tobe approximately .two orders of magnitude smaller than the experimental results.It is apparently unnecessary to take the resonance absorption of bremsstrahlungby the isomeric level into account . Consequently we can neglect the isomer produc-tion via the resonance absorption of bremsstrahlung .

Furthermore,'° 3Rh has no possibility of being excited by the NEET process, sincethe nuclear excited levels in ioaRh are much higher in energy than the extranuclearelectron states ( _<_ 23.2 keV) .

It is concluded that a formula of de Forest and Walecka with the experimentaltransition probability predicts reasonably the total cross section for Coulombexcitation ofnuclei by means ofelectrons even in the case ofrather high target atomicnumber and low incoming energy, where the Born approximation is not explicitlyexpected to be good. These experimental results on '°3Rh validate the estimate ofCoulomb excitation in ' e90s made in the electron-bombarding experiment 3),where the Coulomb excitation was considered as the most probable competitiveprocess with NEET.

Theauthors are greatly indebted to Drs. M. Hatada and K. Matsuda of the OsakaLaboratory of JAERI for kindly operating the accelerator. They wish to expresstheir gratitude to Dr. T. Tabata of the Radiation Center of Osaka Prefecture forhelpful discussions. The support and interest of Dr. H . Baba of the Tokai Establish-ment of JAERI is also appreciated. One of the authors (K.O .) would like to expresshis sincere thanks to the Takahashi Foundation for financial aid, and the NishinaMemorial Foundation for a grant.

References

1) M. Motile, Prog. Theor. Phys . 49 (1973) 15742) K. Otozai, R. Arakawa and M. Monta, Prog . Theor. Phys. SO (1973) 17713) K. Otozai, R. Arakawa and T. Salto, Nucl. Phys. A297 (1978) 974) T, de Forest, Jr . and J. D. Walecka, Adv. in Phys. 13 (1966) 15) Y. Nakai, K. Matsuda and T. Takagaki, Japan Atomic Energy Research InstituteMreport JAERI-M

6702 (1976) p. 806) Y. Nakai and S. Horikiri, Isot . Redut. 2 (1959) 2337) A. R. Frederickson, Air Force Cambridge Research Laboratorien report AFCRL-69-0144 (1969)8) K. F. Koral and A. J. Cohen, NASA txhnical note NASA TN D-2909 (1965)9) T. Tabata, R. Ito and S. Okabe, Nucl. Insu . 94 (1971) 50910) L. Landau, J. of Phys . (USSR) 8 (1944) 20111) T. Tabata and R. Ito, Nucl . Insu. 127 (1975) 42912) J. Jakahik and K. P. Jimgst, Nucl . Insu. 79 (1970) 240, and references therein13) K. Matsuda, private communication

14) J. B. Gumming, National Academy of Sciences report NAS-NS 3107 (1962) p. 2515) C. M. Lederer and V. S. Shirlry, Table of isotopes; 7th ed . (Wilry, New Yorr, 1978)16) L. Wielopolsri, Nucl . lnstr. 143 (1977) 577l7) W. Bothe, Z. Naturforsch . 4a (1949) 54218) D. C. Kocher, Nucl . Data Sheets 13 (1974) 337l9) E. S. Macias, M. E. Phdps, D. G. Sarantitea and R. A. Meyer, Phys. Rev. C14 (1976) 63920) R. H . Pratt, H. K. Tseng, C. M. Lee, L. Kissd, C. MacCallum and M. Riley, Atomic Data and Nucl .

Data Tables m (1977) 175