Phenomenological systematics Phenomenological systematics of the (d,p) cross sectionsof the (d,p) cross sections

A.V.IgnatyukA.V.Ignatyuk

Institute of Physics and Power Engineering, Obninsk, RussiaInstitute of Physics and Power Engineering, Obninsk, Russia

DWBA description of the double deferential cross sections;DWBA calculations of the integral (d,p) cross sections;Empirical approximation of the (d,p) cross sections with

the ALICE-D and EMPIRE-D codes;Phenomenological systematics of the (d,p) cross sections;Phenomenological systematics of the (d,p) cross sections;Structure effects for the enhancement coefficients;Conclusions.

3d CRP Meeting on FENDL-3,Vienna, 6-9 December 2011

4848Ca(d,p): experimental data and the corresponding DWBA descriptionCa(d,p): experimental data and the corresponding DWBA description

W.D.Metz, W.D.Calender,C.R.Bockelman. Phys. Rev.,C12 (1975) 827

4848Ca(d,p): experimental data and the DWBA descriptions Ca(d,p): experimental data and the DWBA descriptions for 9for 9thth and 10 and 10thth levels levels

W.D.Metz, W.D.Calender, C.R.Bockelman. Phys. Rev., C12 (1975) 827

DWBA description of the integral (d,p) cross sections for DWBA description of the integral (d,p) cross sections for 4848Ca and Ca and 5050CrCr

0 5 10 15 20 250

100

200

300

400

500

600

Cro

ss s

ectio

n, m

b

Deuteron energy, MeV

De Waal 1971 SUM 2p3/2 2p1/2 1f5/2

50Cr(d,p) Coetzee 1972

50Cr(d,p) Klein 2001

48Ca(d,p)

Description of the (d,p) and (d,t) cross sections with Description of the (d,p) and (d,t) cross sections with the ALICE-D codethe ALICE-D code

 

 

Naaa

invb

a

b

b

ba gA

C

VE

AK

AE

b

s

s

d

d0127.0)(

)(

12

12 2,

The simple Kalbach formula was used:

where C=3800, Va is the potential well depth, gN is the single-particle level density for neutrons and K is the adjusted parameters. This parameter should be energy dependent to describe the available experimental data !

Experimental data for the Experimental data for the 197197AuAu((d,pd,p))198g198gAu Au crosscross section in comparison section in comparison with various calculationswith various calculations

197Au(d,p)198gAu

0

50

100

150

200

250

300

0 10 20 30 40 50 60

Deuteron energy (MeV)

Cro

ss s

ectio

n (m

b)

Nassiff 1966

Sandoval 1964

Jahn 1973

Long 1985

Wenrong 1989

Tarkanyi 2010 40 MeV

Tarkanyi 2010 20 MeV

ALICE-D

EMPIRE-D

EAF-2007

TENDL-2009

Description of the (d,p) cross sections with the ALICE-D codeDescription of the (d,p) cross sections with the ALICE-D code

5 10 15 20 25 30 35 40

1

10

100

Y90(d,p) Correzza 1971 Cd114(d,p) Tarkanyi 2006 Sn124(d,p)Sn125m Pr141(d,p) Tarkanyi 2008 Ho165(d,p)Ho166g Yb170(d,p)_Hermanne 2006 Alice D Alice D*0.78

Cro

ss s

ectio

n (m

b)

Deuteron energy (MeV)

Phenomenological systematicsPhenomenological systematics

 

 

The analytical function for the description of experimental data was accepted in the following form:

where the factor before the square brackets defines the low-energy increasing part of the (d,p) cross section and the terms in the square brackets characterize the decreasing part. The parameter b determines the effective threshold of the (d,p) reaction and it should be close to the height of the Coulomb barrier

)]/exp()1()/exp([)exp(1

)( 22121 dEadEa

aE

cEb

3/1

2

Ar

Zeb

eff

The mean value of the radius parameter estimated from the experimental data analysis is reff=1.985±0.045 fm.

b.

Experimental data for the Experimental data for the 5959Co(d,p) reaction compared with Co(d,p) reaction compared with various calculationsvarious calculations

Experimental data for the Experimental data for the 197197Au(d,p) reaction compared with Au(d,p) reaction compared with various calculationsvarious calculations

Parameter values estimated from the analysis of Parameter values estimated from the analysis of experimental dataexperimental data

Parameter 59Co(d,p) 197Au(d,p)

a1 751±87 mb 904±121 mb

b 5.13±0.22 MeV 9.86±0.11 MeV

c 0.75 MeV was fixed 0.716±.035 MeV

a20.891±0.011 0.876±.015

d1 7.21±0.61 MeV 7.05±0.84 MeV

d2 37.34±2.76 MeV 35.0 MeV was fixed

Experimental data for the Experimental data for the 141141Pr(d,p) reaction compared with Pr(d,p) reaction compared with various calculationsvarious calculations

Experimental data for the Experimental data for the 181181Ta(d,p) reaction compared with Ta(d,p) reaction compared with various calculationsvarious calculations

Optimal parameter estimated from the analysis of the Optimal parameter estimated from the analysis of the available experimental data.available experimental data.

Other parameters:

c=.75 MeV, a2=0.848,

d1=7.1, d2=35 MeV

Aa 871.06721

Conclusions:Conclusions:

For the deuteron induced reactions the TENDL-2010 evaluations essentially underestimate the (d,p) reaction cross sections for the most of nuclei. There are also unphysical jumps of the cross sections at low energies. So, the corresponding sections of the TENDL-2010 files should certainly be corrected in the process of the FENDL-3D library formation. The phenomenological systematics of the (d,p) cross sections, proposed in the present report, can be recommended as an optimal evaluation of such data for all nuclei and the whole energy region.

Empirical estimation of the (d,t)Empirical estimation of the (d,t)dirdir cross sections for cross sections for 169169TmTm

0 5 10 15 20 25 30 35 400.1

1

10

100

Cro

ss s

ectio

n, m

b

Deuteron energy, MeV

Tarkanyi 2007 Hermanne 2008 EMPIRE ALICE

d,tdir estimation

169Tm(d,p2n)168Tm

Analysis of the Analysis of the 169169Tm(d,x) cross sectionsTm(d,x) cross sections

0 5 10 15 20 25 30 35 400.1

1

10

100

1000

d,p3n

d,p2n

d,2n

Cro

ss s

ect

ion

, mb

Deuteron energy, MeV

2006-Tarkanyi 169Yb_Herm2008 Hermanne 2008 167Tm_Herm2008 Alice-D Empire-D

169Tm(d,x)167Tm_cum