Perturbation theory in nuclear reactions

Brown, G. E.; Dominicis, C T de; Langer, Jan

doi:10.1016/0003-4916(59)90079-x

Cited by 19 publications

(5 citation statements)

References 13 publications

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“…In our case only this condition allows the first term in the series (11) to be retained, omitting the rest. One can easily see that this condition together with (25) allows the cS-shape form (4,5) to be used in the collision integral and the integration over co in (18) to be carried.…”

Section: St N = I S -+ (E -# P; T R) [ 1 -N(p R T)] + Is + -(S mentioning

confidence: 97%

“…One should note that an analogous version of perturbation theory based on energy averaging A e>/~ was considered [18,19] in the derivation of the optical model. We used the same method in deriving kinetic equations [13].…”

Section: Aementioning

confidence: 99%

“…In order to proceed further, one needs to assume the validity of perturbation theory in the two-body interactions V. That is, one should assume these interactions to be small and calculate the stoss integral (18) in the first non-vanishing order of perturbation theory. Then one can see [12] that the Green's functions would still retain the 6-like behaviour of the ideal gas (4, 5), but the 6(co-e+#) factors should be substituted by:…”

Section: (7)mentioning

confidence: 99%

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The physical and mathematical foundations of the intranuclear cascade model algorithm

Бунаков

Matvejev

1985

Z Physik A

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The physical and mathematical approximations underlying the intranuclear cascade model (INC) algorithm are considered here. The INC algorithm is shown to be a version of Monte-Carlo calculations for multiple integrals which provide the solutions of the system of coupled equations for many-body distribution functions. The conditions under which these equations are derived from the Schr6dinger many-body equations are analysed, with special emphasis on the finite size of the nuclear system.

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Section: St N = I S -+ (E -# P; T R) [ 1 -N(p R T)] + Is + -(S mentioning

confidence: 97%

Section: Aementioning

confidence: 99%

Section: (7)mentioning

confidence: 99%

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The physical and mathematical foundations of the intranuclear cascade model algorithm

Бунаков

Matvejev

1985

Z Physik A

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“…Equation (14) tells us that the unlike pairs are coupled with each other by the particle-hole interaction matrix F, and also coupled with two pair states {(ii-p) and (li-n) or (p-p)}, which are graphically illustrated in Fig. 1.…”

Section: K Ikedamentioning

confidence: 99%

“…When we neglect the term of X in Eq. (14), the equation of pair amplitude ~J(ac) is linearized as follows: (16) with EJ== (EJ-U) being the excitation energy from the ground state of target. In this case, we can obtain the eigenvalues EJn's and.…”

Section: K Ikedamentioning

confidence: 99%

Collective Excitation of Unlike Pair States in Heavier Nuclei

Ikeda

1964

Prog. Theor. Phys.

120

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The neutron-hole-proton pair (n-p) correlations in heavier nuclei are studied on the basis of the j-j coupling shell model. It is shown that the even parity states as the coherent mixture of many unperturbed (n-p) states are pushed up by the (n-p) repulsive interactions with T=l. The isobaric state T_l'f£ 0 ) can ,be interpreted as a coherent state with Jrr=O+. The coherent states with non-zero spin arise in the high excited energy region but not higher than that of the isobaric state. They may be strongly excited by the (p, n) reaction.The actual numerical calculations assuming zero-range forces are carried out for the J,.. = 1 + states of the nucleus Bi208 which can be produced by the (p, n) reaction using the target nucleus Pb 2 0 8 . The transition strength due to the operator Y_=2}ri-ai concentrates i in the higher energy region, although the spin-orbit splitting plays an important part for distributing the transition strength over the wider energy region.Recently a series of (p, n) reaction experiments 1 >' 2 ),s) were carried out, in which the resonance peaks in excitation functions were observed. Since then, the theoretical considerations have been made by Lane and Soper 4 >' 5 > in order to understand why the isobaric state occurs even in medium and heavier nuclei and they have discussed in detail the properties of the isobaric and the isobaric configuration states.In a previous letter, 6 > the isobaric state :z=ri_jif.l 0 ) =T _J tf!o) can be interpreted i as a coherent mixture of (N-Z) neutron-hole-proton (in short, 7z-p) pair states with J" = o+' which exhibits a characteristic feature of the isospin collective oscillation. The picture of the collective motion for unlike pair states in terms of the shell model can be easily extended 7 l to the other coherent states which may be excited by (p, n) reaction. The extended treatment is very useful for the study of the neutron-proton correlation in nuclei. The purpose of this paper is to study the collective states with the unlike pair excitations, which should have the lower excitation energies than that of the isobaric state T -I P: 0 ). It is easily seen that many unperturbed pair states with even parity exist in the region of the excitation energy lfiw in terms of the harmonic oscillator model for heavier nuclei because of many excess at University of The unlike particle-hole interaction matrix is equal to the like one for T = 1. Provided that the zero range forces in the form of Eq. (4) are used, the direct term D is equal to the exchange term E and therefore F= 2E. In the case of finite range potential, D isgenerally smaller than E. We can effectively write at University of

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Sul meccanismo delle reazioni nucleari

Facchini¹

1960

Seminario Mat. e. Fis. di Milano

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Perturbation theory in nuclear reactions

Cited by 19 publications

References 13 publications

The physical and mathematical foundations of the intranuclear cascade model algorithm

The physical and mathematical foundations of the intranuclear cascade model algorithm

Collective Excitation of Unlike Pair States in Heavier Nuclei

Sul meccanismo delle reazioni nucleari

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