Transcript NUCLEAR LEVEL DENSITIES NEAR Z=50 FROM NEUTRON …

NUCLEAR LEVEL DENSITIES NEAR Z=50 FROM
NEUTRON EVAPORATION SPECTRA IN (p,n)
REACTION
B.V.Zhuravlev, A.A.Lychagin, N.N.Titarenko
State Scientific Center of Russian Federation - Institute for Physics and Power
Engineering, 249033 Obninsk, Kaluga Region, Russia
The experimental data on the nuclear level densities for many nuclei are
derived, in the main, from the analysis of low-lying level and neutron resonance
data. However, this information is limited to rather narrow ranges of excitation
energy, and spin, and its extrapolation can lead to essential errors both in absolute
value of the nuclear level density and its energy dependence, especially, in
transition field from well-identified discrete states to continuum part of excitation
spectrum. Obviously, it is necessary to attract other experimental methods of the
nuclear level density determination with scope of more wide ranges of excitation
energy, spin and (N-Z) value. Such method has been the study of the spectra of
particles emitted in nuclear reactions. In this case the type of reaction and the
energy of incident particles should be chosen so that the contribution of
nonequilibrium processes was minimum. For the middle and heavy nuclei these
conditions are best satisfied with (p,n) reaction at proton energy up to 11 MeV.
In the present work the differential neutron emission cross-sections for
(p,n) reaction on nuclei of 116Sn, 118Sn, 122Sn, 124Sn, in proton energy range of (7 - 11)
MeV have been measured and analyzed in the framework of statistical theory of
nuclear reactions to study the features of nuclear level density near filled shell
Z=50 and its isotopic dependence.
Experiment
10
15
14
10
10
Ep=6.86 MeV
13
Ep=6.87 MeV
12
10
Ep=8.03 MeV
10
11
Ep=8.04 MeV
10
10
Ep=8.65 MeV
Ep=9.1 MeV
9
8
10
Ep=9.09 MeV
Ep=9.52 MeV
10
d/dEn, mb/MeV
d /dEn, mb/MeV
10
7
Ep=10.18 MeV
10
5
6
10
Ep=10.17 MeV
4
10
Ep=10.70 MeV
Ep=10.71 MeV
10
3
2
10
Ep=11.11 MeV
Ep=11.12 MeV
10
10
1
0
10
-1
-2
0
1
2
3
4
5
6
En, MeV
Angle-integrated neutron emission
spectra from 116Sn(p,n)116Sb
reaction.
10
0
1
2
3
4
5
6
En, MeV
Angle-integrated neutron emission
spectra from 118Sn(p,n)118Sb
reaction.
7
Angle-integrated neutron emission
spectra from 122Sn(p,n)122Sb
reaction.
Angle-integrated neutron emission
spectra from 124Sn(p,n)124Sb
reaction.
Scheme of a compound
nucleus reaction for specific
example.
Data analysis
The method of nuclear level density determination from emission spectra is based
on the fact that the nuclear level density is one of the most critical component of statistical
model calculations. The procedure of nuclear level density determination consisted in
following:
The model parameters of the level density are adjusted such that the crosssection calculated by means of Hauser-Feshbach formula fits the measured value in the
energy range of well-known low-lying levels. It means that the total decay width of
compound nucleus is determined.
Using, at first, the chosen model of the level density and, in next iterations, the
absolute values of the level density, the differential cross-section for continuum part of
spectrum is calculated and the absolute level density is determined in a wide range of
excitation energy from the best fit with the spectra measured.
d 2 ( E0 , E2 , ) 1
 2 
dE2d
4K0 kJ1
 
 ( Tl , j 
c
l, j

l0 j0l2 j2
2J1  1
 Bk (l0 , S0 , j0 , J 0 , J1 )   Bk (l2 , j2 , S2 , J 2 , J1 )    ( E0  Q ,n  E2 , J 2 )  Pk (cos ),
(2S0  1)  (2 J 0  1)
Tl0 j0 ( E0 )  Tl 2 j2 ( E2 )

 Tl , j   ( E0  Q ,n  E2 , J 2 )  dU
,
l , j,J Uc
Bk (l , S , j , J f , J i )  (1)
J f  Ji S
 (2 J i  1)  (2 j  1)  l0l0 K 0 W ( J i J i jj; KJ f )  W ( jjll; KS )
Results: The extracted level densities for 116Sb, 118Sb, 122Sb, 124Sb excited in reactions studied are
presented in the next figs. The total uncertainties of the level densities are about 13 to 18 %.
7
10
7
10
6
10
6
10
5
5
10
4
10
4
 (U), 1/MeV
 (U), 1/MeV
10
3
10
2
10
10
3
10
2
10
1
10
1
10
0
10
0
0
2
4
6
U, MeV
Nuclear level density of 116Sb.
8
10
0
2
4
U, MeV
6
Nuclear level density of 118Sb.
Experimental data: o - present work, histogram - low-lying levels data. The curves are
calculated results: dotted - GSN, dash-dotted - BSFG, dashed - G-C systematics.
8
10
 (U), 1/ MeV
10
7
10
7
10
6
10
5
10
4
10
3
10
2
10
1
6
5
10
4
10
3
10
2
10
1
10
0
 (U), 1/MeV
10
0
1
2
3
4
5
6
U, MeV
Nuclear level density of 122Sb.
7
8
0
2
4
6
8
10
U, MeV
Nuclear level density of 124Sb.
Experimental data: o - present work, histogram - low-lying levels data, closed square - neutron
resonance data. The curves are calculated results: dotted - GSN, dash-dotted - BSFG,
dashed - G-C systematics.
For a sequence of excited nuclei of Sb (Z=51, N=65, 67, 71, 73) is observed the essential
decreasing of the nuclear level density with increasing of (N-Z). This decrease may be
explained by effect connected with isospin. For nuclei with number of neutrons N and protons
Z, the range of allowed isospin values is from Tmin=(N-Z)/2 and above. With increase of (N-Z)/2,
the range of allowed isospin values will be shorten and the total number of excited singleparticle levels have to decrease monotonically. Such approach predicts the dependence of the
nuclear level density parameter "a" not only from A, but and from (N-Z).
ã = A/exp[(N-Z)2]
(1)
16
a, MeV
-1
18
14
12
12
14
16
18
(N - Z)
20
22
24
Dependence of nuclear level density parameter “ã” from (N-Z) for Sb isotopes. o –
present work,   [11]. Curve – calculation on eq. (1) with  = 0.154 and  = 0.00064.
Nuclear level density parameters
Model
G–C
GSN
Parameter
Nucleus
ã
o
W

Cv
2+
BSFG c)
a

Ex
T
Eo
a

Ec
NL
116Sb
a)
b)
15.6
11.2
0.68
1.12
0.25
0.25
0.082
0.082
0.037
0.037
1.00
1.00
19.0
17.4
0
0
1.77
2.64
0.41
0.50
-0.30
-0.56
19.0
15.3
-0.05
-0.78
0.95
0.95
24
24
118Sb
a)
b)
16.9
11.4
0.61
1.11
0.52
0.52
0.082
0.082
0.037
0.037
1.00
1.00
20.5
17.9
0
0
2.51
2.59
0.44
0.50
-0.72
-0.85
20.4
15.2
-0.05
-0.92
0.32
0.32
12
12
122Sb
a)
b)
15.6
11.7
0.00
0.00
-0.34
-0.34
0.081
0.081
0.037
0.037
1.00
1.00
16.6
16.5
0.22
0.22
3.35
3.39
0.55
0.55
-0.75
-0.77
16.2
14.9
0.10
-1.21
1.07
1.07
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28
124Sb
a)
b)
12.4
11.9
0.69
1.08
-1.23
-1.23
0.080
0.080
0.037
0.037
1.00
1.00
15.6
15.3
0
0
4.36
4.49
0.65
0.66
-1.55
-1.61
15.4
14.0
-0.50
-1.39
0.48
0.48
26
26
a) Parameters corresponding to the best fit spectra calculated and measured,
b) Parameters recommended in systematics GSN, BSFG, G - C,
c) BSFG calculations have been carried out with rigid body moment of inertia.
3
10
2
E=16.3 MeV
2
 (En), mb/MeV
10
1
10
 (En),
mb/MeV
10
E=18.3 MeV
1
10
0
10
0
10
10
-1
10
-2
-1
10
0
1
2
3
4
5
6
7
8
En, MeV
Neutron spectra from 115In(α,n )118Sb
reaction at Еα =16.3 MeV.
0
1
2
3
4
5
6
7
8
9
10
En, MeV
Neutron spectra from 115In(α,n )118Sb
reaction at Еα =18.3 MeV.
10
10
3
 (En), mb/MeV
 (En), mb/MeV
10
3
10
2
2
E=26.8 MeV
10
10
1
0
-1
10
-2
E=45.2 MeV
10
1
10
0
-1
10
10
0
5
10
15
En, MeV
Neutron spectra from 115In(α,xn )118Sb
reaction at Еα =26.8 MeV.
0
5
10
15
20
25
30
35
En, MeV
Neutron spectra from 115In(α,xn )118Sb
reaction at Еα =45.2 MeV.
Conclusion:
1)
2)
3)
4)
5)
6)
The neutron emission spectra in (p,n) reaction on isotopes of 116Sn,
118Sn, 122Sn, 124Sn have been measured and analyzed in the framework
of statistical equilibrium and preequilibrium models of nuclear reactions.
The absolute nuclear level densities of 116Sb, 118Sb, 122Sb, 124Sb, theirs
energy dependences and model parameters are determined.
In the excitation energy range of (0-2) MeV, the energy dependences of
the nuclear level density exhibit a structure that is associated with the
shell unhomogeneties of a single-particle state spectrum.
The isotopic dependence of the nuclear level density is found out.
It is shown also that the obtained data differ essentially from the
predictions of the nuclear level density model systematics.
Use of these data on nuclear level densities of Sb isotopes has allowed
reliably to calculate the contribution of equilibrium neutron emission in
115In(,xn) reaction at -particle energies of 16, 18, 27 and 45 MeV, that
was very important for determination of nonequilibrium neutron
emission in this reaction.