Three-body approach to the single-scattering optical potential (original) (raw)
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Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions
Annals of Physics, 1979
Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.
The concept of an optical potential as a physical entity that governs the scattering of a single particle by a composite target is an intuitively appealing phenomenological concept that goes back to the early days of nuclear physics. In principle, the scattering of a nonrelativistic, quantum-mechanical particle off an N -particle target is a many-body problem and governed by the (N + 1)-particle Schrödinger equation. In the so-called optical model [1], the elastic scattering problem is alternatively described by an effective single-particle Schrödinger (or Lippmann-Schwinger) equation. All effects of the interaction of the projectile particle with the target are contained in the so-called optical potential. In general, this optical potential has to be a very complicated object: It becomes a nonlocal operator because exchange and rearrangement of target particles have to be considered. An energy dependence has to account for possible excitations of the target and if inelastic scattering is energetically possible, the optical potential is nonhermitian in order to describe the loss of scattering amplitude into the inelastic channels. One major technical advantage of using optical potentials in numerical calculations is that the scattering problem can be separated from the many-body problem and the latter can be treated using bound-state techniques.
Equivalent local potentials to multiple scattering calculations of nucleon-nucleus scattering
Physical Review C, 1994
Local phase equivalent interactions to the nonlocal Kerman, McManus, and Thaler multiple scattering nucleonnucleus optical potentials are determined. Both firstand second-order contributions in the free nucleon-nucleon transition amplitude are included. The second order terms modify the derived potentials in a nontrivial way and reduce the strengths of the real and imaginary central potentials in the nuclear interior. The nonlocality of the firstand second-order multiple scattering potentials is quantified by the evaluation of an associated Percy factor. Calculations give a mean free path of A = 3-4 fm for 100-200 MeV incident nucleons on O.
MCAS: A Multichannel Algebraic Scattering Theory of Low Energy Nucleon-Nucleus Reactions
AIP Conference Proceedings, 2005
Low energy cross sections from the collision of nucleons with light mass nuclei show sharp as well as broad resonances upon a smooth, energy dependent background. Those resonances may correlate to states in the discrete spectrum of the target. To interpret scattering data of that type requires a complex coupled channel reaction theory. A suitable and convenient theory has been developed and forms the MCAS; a Multi-Channel Algebraic Scattering theory. With MCAS, scattering matrices are determined by using sturmian-state expansions of the relevant nucleon-nucleus potential matrix. MCAS yields a matrix form of the Green function for scattering from which extraction of the sub-threshold (compound nucleus) bound-state spin-parity values and energies is facile. The procedure also gives the energies and widths of resonances in the scattering regime. Applications for both proton and neutron scattering form 12 C are presented.
An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering
Nuclear Physics A, 2003
Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated multichannel interactions between the colliding nuclei. Associated with such expanded multichannel interactions are algebraic multichannel scattering matrices. The matrix structure of the inherent Green functions not only facilitates extraction of the sub-threshold (compound nucleus) bound state spin-parity values and energies but also readily gives the energies and widths of resonances in the scattering regime. We exploited also the ability of the sturmian-expansion method to deal with non-local interactions to take into account the strong non-local effects introduced by the Pauli principle. As an example, we have used the collective model (to second order) to define a multichannel potential matrix for low energy neutron-12 C scattering allowing coupling between the 0 + 1 (ground), 2 + 1 (4.4389 MeV), and 0 + 2 (7.64 MeV) states. The algebraic S matrix for this system has been evaluated and the sub-threshold bound states as well as cross sections and polarizations as functions of energy are predicted. The results are reflected in the actual measured data, and are shown to be consistent with expectations as may be based upon a shell model description of the target and of the compound nucleus.
A multichannel quasi-separable potential approach to nucleon-nucleus scattering
Nuclear Physics A, 1978
AbsMct : A quasi-separable potential model for two-body multichannel scattering is developed . Spin and Coulomb effects are taken into account. By a suitable choice of the separable nuclear interactions we arrive at simple analytic expressions for thé transition amplitudes . Our model is applied to the study of the n-' 2C and p-isC scattering processes . Effects arising from the excitation of the target nucleus are well reproduced.
A Fully Algebraic Model for Multichannel Low Energy Nucleon-Nucleus Scattering
Journal of Nuclear Science and Technology, 2002
Compound resonances in nucleus-nucleus scattering (bound states in the continuum) relate to bound states in the subsystems. Both types of resonances can be studied in a unified and general framework by a model for the scattering that uses Sturmian expansions of multichannel interactions between the colliding nuclei. Associated with such expanded multichannel interactions are algebraic multichannel scattering matrices. As an example, we have used the collective model (to second order) to define the interaction potentials for low energy neutron-12C scattering allowing coupling between the ground ot, 2t (4.44 MeV), and ot (7.64 MeV) states. The algebraic S matrix for this system then has been evaluated and cross sections as a function of energy obtained Resonance structures occur naturally and are reflected in the actual measured data.
A perturbation theory of nuclear scattering including recoil
Annals of Physics, 1970
The theory of elastic nucleon-nucleus scattering is generalized to include the recoil of the nucleus. The exact T matrix is obtained as the residue of a second-order pole of an off-diagonal single particle Green function. A perturbation expansion is made using the intrinsic Hamiltonian and a new generalization of the Goldstone expansion for the ground state. This makes the extraction of the delta function for overall momentum conservation simple. A linked cluster expansion is derived for the Green function and two types of recoil corrections are identified, linked and unlinked. A new theorem is proved, expressing the exponent of a one body operator in a convenient way. This allows us to show that terms with linked corrections cannot contribute to the scattering. The T matrix including recoil is then expressed as the T matrix of the generalized optical potential calculated in the usual way (but using the intrinsic Hamiltonian) multiplied by a correction factor due to recoil. An approximation scheme for calculating the correction factor is presented and suggestions are made for improving existing calculations. 1. JNTRODUCTION * This work is based on a thesis submitted in partial fulfillment for the degree of Ph.D at
Microscopic optical potential with two and three body forces for nucleon–nucleus scattering
EPJ Web of Conferences, 2014
The proton-nucleus optical potentials generated by folding the calculated complex, density and energy dependent g-matrices (with and without three-body forces (TBF): Urbana IX (UVIX) and TNI) over the target nucleon density distributions obtained from the relativistic mean field theory, are used for the calculation of the differential cross section / d d σ θ , polarization y A , spin rotation function (Q). for 65 and 200 MeV polarized proton incident on 40 Ca and 208 Pb. The agreement with the experiment is rather impressive. It is found that the inclusion of TBF (Urbana IX (UVIX) and TNI) reduces the strength of the central part of the optical potential in the nuclear interior and affects the calculated spin-orbit potential only marginally and leads to an improvement in the agreement with the corresponding experimental results.
Multichannel multiple-scattering theory with general potentials
Physical Review B, 1990
%e outline a many-body description of the photoemission and photoabsorption processes that incorporates the multichannel treatment of the atomic dynamical excitations into the framework of multiple-scattering (MS) theory. This generalization is a most natural one, in that the internal structure of the atomic constituents of the physical system under study is taken into account by the introduction of an interchannel atomic t matrix that fixes the probability amplitude of a particular excitation (channel) of the internal degrees of freedom of the atom by the photoelectron impinging on it. For the rest the MS structure of the theory is left unchanged, provided the propagation vector of the photoelectron between successive scattering events is changed according to the energy loss suffered. In this way the interplay between excitation dynamics and electronic and geometrical structure of the ground state is elucidated. At the same time this approach provides a theoretical model for the study of the evolution from the adiabatic to the sudden regime. In this context we describe a new MS expansion that reproduces the results of the sudden approximation for photoemission and photoabsorption cross sections in the limit of high photoelectron energies. As expected, the expansion parameter that controls the crossover between the two regimes is substantially the maximum eigenvalue of the interchannel atomic t matrix (T,)LL (aWa'), where a is a channel index and L is an angular-momentum index: If this quantity is much less than one, then the deviations from the sudden approximation are negligible. Physical applications of the theory are briefly described.