NUCLEAR REACTION MODELS FOR SYSTEMATIC ANALYSIS OF FAST NEUTRON INDUCED

(n,p) REACTION CROSS SECTIONS

M.Odsuren, J.Badamsambuu, G.Khuukhenkhuu

Nuclear Research Center, National University of Mongolia, Ulaanbaatar, Mongolia

MOTIVATION

Investigation of fast neutron induced charged particle emission reactions is important:

1. Fundamental nuclear physics study: – The study of nuclear reactions mechanisms – Nuclear structure

2. Fission and fusion reactors technology:– Radiation damage – Residual radioactivity – Hydrogen and helium gas production

Systematical analysis of neutron cross sections is of interest: 1. To evaluate of neutron cross sections2. To estimate of authenticity for experimental data

Statistical Model: J.M.Blatt, V.F.Weisskopf, Theoretical Nuclear Physics, John Wiley and Sons, New York, (1952)

Compound Mechanism: N.Bohr, Nature, v.137 (1936), p.344

Pre-equilibrium Mechanism: J.Griffin, Phys.Rev.Lett. vol.17, 1966, p.478 Exciton Model

Direct Reaction Mechanism: J.R.Oppenheimer, M.Philips. Phys.Rev., v.48, Plane Wave Born Approximation N6, 1935, p.500

V.N. Levkovsky, Sov.J.Nucl.Phys. 18, N4, 1973, p.705 Empirical formula (n,p) and (n,) at En=14-15 MeV

Here: C=0.73 and, K=33 are fitting parameters.

A

ZNK

eArCpn

23/12

0 )1(),(

G.Khuukhenkhuu, JINR preprint. E3-93-205, Dubna, 1993

A

ZNK

comnp eRC

12)(

pVAA

ZC

4/33/1

121exp

4K

Here:

R, Z, N and A - radius, proton, neutron and mass numbers of target nuclei

- Wavelength of incident neutrons divided by 2Vp - Coulomb potential for protons

- Thermodynamic temperature of nuclei

and =i-f - Сonstants of Weizsacker’s formula.

G.Khuukhenkhuu, G.Unenbat, M.Odsuren et al. JINR Preprint, E3-2007-25,Dubna, 2007, -12p.

(1)

– Statistical Model:

– Exciton Model:

3

3

0

22

6

)(

)(2)(3.68

nn

pnpnpnr

prenp

BE

VQE

AK

MER

)( nr E3

0 MeV 400KpM

nE nB

npQ

dirnp

prenp

comnp

totnp

n

np2

0

dir

np E

Q1RC

Where 0C can be determined as best fitting the experimental data parameter.

Theoretical total (n,p) cross section:

(2)

(3)

G.Khuukhenkhuu, G.Unenbat, M.Odsuren et al.JINR Preprint, E3-2007-26, Dubna, 2007, -5p.

Where:

-Neutron induced reaction total cross section

- Mass of proton

and - Kinetic and binding energy of neutron

- Reaction energy

G.Khuukhenkhuu, G.Unenbat, M.Odsuren et al.JINR Preprint, E3-2007-27, Dubna, 2007, -7p

– Plane Wave Born Approximation:

SYSTEMATICS OF THE (n,p) REACTION CROSS SECTIONS

En (MeV) K C

6 75.2 17.5

8 62.8 11.9

10 52.1 6.80

13 38.8 2.74

14.5 37.3 2.43

16 33.5 1.42

18 22.4 0.39

20 17.9 0.25

En=20 MeV

C = 0.25K=17.9

1.E-03

1.E-02

1.E-01

1.E+00

0.02 0.06 0.10 0.14 0.18 0.22(N-Z+1)/A

n

p/

(R+l

)2

En=14.5 MeV

C = 2.43K=37.3

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0.02 0.06 0.10 0.14 0.18 0.22

N-Z+1/A

np

/(R

+l )

2

En=6 MeV

C = 17.5K=75.2

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0.02 0.06 0.10 0.14(N-Z+1)/A

np/ (

R+l )

2

Statistical model (n,p) cross sections and experimental data:

COMPARISON OF EXPERIMENTAL AND THEORETICAL (n,p) CROSS SECTIONS

En=6 MeV

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.02 0.06 0.10 0.14(N-Z+1)/A

np(m

b)

Experiment

Compound

En=20MeV

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.02 0.06 0.10 0.14 0.18 0.22

(N-Z+1)/A

np (m

b)

Experiment

Compound

En=14.5 MeV

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.02 0.06 0.10 0.14 0.18 0.22N-Z+1/A

(m

b)

Experiment

Compound

A

1ZNK

2com

np eRC

)(

Exciton model (n,p) cross sections and experimental data:

En=14.5 MeV

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.00 0.05 0.10 0.15 0.20 0.25

(N-Z+1)/A

n

p (m

b)

Experiment

Pre-equilibrium

En=6 MeV

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.02 0.06 0.10 0.14(N-Z+1)/A

np (

mb

)

Experiment

Pre-equilibrium

En=20MeV

1.E+00

1.E+01

1.E+02

1.E+03

0.02 0.06 0.10 0.14 0.18 0.22

(N-Z+1)/A

n

p(b

m)

Experiment

Pre-equilibrium

3

nn

3pnpn

0

pnr

2

2

6pre

npBE

VQE

AK

M2ER368

)(

)()(.

PWBA (n,p) cross sections and experimental data:

En=14.5 MeV

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.00 0.05 0.10 0.15 0.20 0.25

(N-Z+1)/A

np

(mb)

Experiment

Direct

En=6 MeV

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.02 0.06 0.10 0.14(N-Z+1)/A

np(m

b)

Experiment

Direct

En=20MeV

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0.02 0.06 0.10 0.14 0.18 0.22

(N-Z+1)/A

np (m

b)

Experiment

Direct

n

np2

0

dir

np E

Q1RC

The total (n,p) cross sectiondirnp

prenp

comnp

totnp

The theoretical total (n,p) cross sections are satisfactorily in agreement with experimental values for En=6, 14.5 and 20 MeV. Also, in the case of En=8, 10, 13, 16 and 18 MeV neutrons we have almost the same results.

En=14.5 MeV

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.00 0.05 0.10 0.15 0.20 0.25

(N-Z+1)/A

np

(mb)

Experiment

Comp+Pre+Dir

En=6 MeV

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.02 0.06 0.10 0.14(N-Z+1)/A

np( m

b)

Experiment

Comp+Pre+Dir

n

np20

dirnp E

Q1RC

3

3

0

22

6

)(

)(2)(3.68

nn

pnpnpnr

prenp

BE

VQE

AK

MER

A

ZNKcom

np eRC1

2)(

En=20MeV

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

0.02 0.06 0.10 0.14 0.18 0.22

(N-Z+1)/A

n

p (m

b)

Experiment

Com+Pre+Dir

CONCLUSION

1. Using the statistical model, exciton model and PWBA are deduced formulae for the fast neutron induced (n,p) reaction cross sections.

2. The formulae were used for systematical analysis of fast neutron induced (n,p) reaction cross sections.

3. It was shown that the theoretical and experimental total (n,p) cross sections for En=6-20 MeV are satisfactorily in agreement.

Thank you for your attention

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NUCLEAR RESEARCH CENTERNEUTRON GENERATOR

E=14MeV11010 sF

NUCLEAR RESEARCH CENTER252Cf-NEUTRON SOURCE

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scmn10F

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8typroductivi

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10010ysensitivit

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eV180resolution

.

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