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