NUCLEAR LEVEL DENSITIES NEAR Z=50 FROM NEUTRON EVAPORATION SPECTRA IN (p,n)

REACTIONB.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

Angle-integrated neutron emission spectra from 116Sn(p,n)116Sb reaction.

Angle-integrated neutron emission spectra from 118Sn(p,n)118Sb reaction.

Angle-integrated neutron emission spectra from 122Sn(p,n)122Sb reaction.

Angle-integrated neutron emission spectra from 124Sn(p,n)124Sb reaction.

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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 cross-section 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.

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 %.

Nuclear level density of 116Sb.

Experimental data: o - present work, histogram - low-lying levels data. The curves are calculated results: dotted - GSN, dash-dotted - BSFG, dashed - G-C systematics.

Nuclear level density of 118Sb.

Nuclear level density of 122Sb. 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.

Dependence of nuclear level density parameter “ã” from (N-Z) for Sb isotopes. o – present work, Curve – calculation on eq. (1) with = 0.154 and = 0.00064.

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 single-particle 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)

Model GSN G – C BSFG c)

ParameterNucleus

ã o W Cv 2+ a Ex T Eo a Ec NL

116Sb a) b)

15.6 11.2

0.681.12

0.25 0.25

0.0820.082

0.037 0.037

1.001.00

19.017.4

0 0

1.772.64

0.41 0.50

-0.30-0.56

19.015.3

-0.05-0.78

0.950.95

2424

118Sb a) b)

16.911.4

0.611.11

0.52 0.52

0.0820.082

0.037 0.037

1.001.00

20.517.9

0 0

2.512.59

0.44 0.50

-0.72-0.85

20.415.2

-0.05-0.92

0.320.32

1212

122Sb a) b)

15.611.7

0.000.00

-0.34-0.34

0.0810.081

0.037 0.037

1.001.00

16.616.5

0.220.22

3.353.39

0.55 0.55

-0.75-0.77

16.214.9

0.10-1.21

1.071.07

2828

124Sb a) b)

12.411.9

0.691.08

-1.23-1.23

0.0800.080

0.037 0.037

1.001.00

15.615.3

0 0

4.364.49

0.65 0.66

-1.55-1.61

15.414.0

-0.50-1.39

0.480.48

2626

Nuclear level density parameters

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.

Neutron spectra from 115In(α,n )118Sb reaction at Еα =16.3 MeV.

Neutron spectra from 115In(α,n )118Sb reaction at Еα =18.3 MeV.

Neutron spectra from 115In(α,xn )118Sb reaction at Еα =26.8 MeV.

Neutron spectra from 115In(α,xn )118Sb reaction at Еα =45.2 MeV.

Conclusion:

1) 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.

2) The absolute nuclear level densities of 116Sb, 118Sb, 122Sb, 124Sb, theirs energy dependences and model parameters are determined.

3) 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.

4) The isotopic dependence of the nuclear level density is found out.5) It is shown also that the obtained data differ essentially from the

predictions of the nuclear level density model systematics.6) 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.