Semiclassical Distorted Wave Research Articles

-Nucleus Potential and (K-, K+) Inclusive Spectrum at - Production Threshold Region

The $(K^-,K^+)$ $\Xi^-$ production inclusive spectrum is reinvestigated in view of the very weak $\Xi$-nucleus potential predicted by microscopic calculations with the SU$_6$ quark-model baryon-baryon interaction. The inclusive spectrum is evaluated by the semiclassical distorted wave (SCDW) method. The explicit comparison of the strength function with that of the Green-function method demonstrates the quantitative reliability of the SCDW approximation. It is presumed that the presently available data at the $\Xi$ production threshold region does not necessarily imply the attractive strength of about 15 MeV for the $\Xi$-nucleus potential in a conventional Woods-Saxon form. Instead, an almost zero potential is preferable.

Quenching of the analyzing power for inclusive quasielastic (p→,p') scattering

Within the context of a nonrelativistic semiclassical distorted wave (SCDW) model, we demonstrate that the experimentally observed reduction of the inclusive quasielastic $^{208}\mathrm{Pb}$($\stackrel{\ensuremath{\rightarrow}}{p},{p}^{'}$) analyzing power relative to the value for free $NN$ scattering, at incident laboratory kinetic energies of 290 and 200 MeV and at the centroid of the quasielastic peak, is mainly attributed to nuclear medium modifications of the $NN$ effective interaction and also nuclear distortion effects on the scattering wave functions. In addition, the SCDW model also provides a satisfactory quantitative description of the unpolarized double differential cross section.

Strength of the Single-Particle Potential in Nuclei from Semiclassical Distorted Wave Model Analysis of the ( -,K+) Inclusive Spectrum

Semiclassical distorted wave model is developed to describe $(\pi^-,K^+)$ inclusive spectra related to $\Sigma^-$-formation measured at KEK with $p_\pi =1.2$ GeV/c. The shape and magnitude of the spectrum on $^{28}$Si target are satisfactorily reproduced by a repulsive $\Sigma$-nucleus potential, the strength of which is of the order of 30$\sim$50 MeV. This strength is not so strong as more than 100 MeV suggested by the estimation presented in the report of the experiment.

Effect of nucleon momentum distribution on the calculation of semiclassical distorted wave model

The semiclassical distorted wave(SCDW)model is applied to the analysis of the multistep direct processes of 90Zr(p,p′x) at 80 and 160MeV incident energies with the single particle momentum distribution of target nucleons given by the coherent density fluctuation model. The calculated double differential cross sections are compared with the experimental data and the results of the previous SCDW model calculations. The agreement of the calculated double differential cross sections with the experimental data is improved, compared with the previous calculations. The effect of the momentum distribution of target nucleons on the calculated cross sections is discussed.

Semiclassical Distorted Wave Model Analysis of Inclusive (N, N’x) Reactions for Incident Energies up to 400 MeV

The semiclassical distorted wave (SCDW) model with the Wigner transform of a one-body density matrix is applied to analyses of multistep direct processes in (p, p’x) reactions on 12C, 90Zr, and 197Au at incident energies near 150 MeV, and 392 MeV (p, p’x) and 346 MeV (p, nx) reactions on 40Ca. The calculations show good agreement with experimental double-differential cross sections over a wide mass range of target nuclei, except at backward angles.

Continuum Cross Sections for Proton-induced Reactions on Biologicaïly-important Target Nuclei

Continuum spectra from the (p, p′) reaction on 12C, 14N and 16O at incident energies of 150 and 200 MeV have been measured at scattering angles from 20° to 150°. The angular distributions at several emission energies are compared with theoretical predictions by means of the semi-classical distorted wave (SCDW) model. It is found that a statistical multistep direct (MSD) interpretation is appropriate also for these very light target nuclei.

Cross sections and polarization observables for the40Ca(p,n)reaction at 345 MeV and multistep contributions in the continuum

The double-differential cross sections and analyzing powers over an angular range of $30\ifmmode^\circ\else\textdegree\fi{}l~{\ensuremath{\theta}}_{\mathrm{lab}}l~75\ifmmode^\circ\else\textdegree\fi{},$ and the induced polarizations P and polarization transfer values ${D}_{\mathrm{NN}}$ at $30\ifmmode^\circ\else\textdegree\fi{}$ and $40\ifmmode^\circ\else\textdegree\fi{}$ for the ${}^{40}\mathrm{Ca}(p,n)$ reaction are measured at a bombarding energy of 345 MeV. The data are compared with theoretical calculations in a semiclassical distorted wave (SCDW) model employing through three- and two-step contributions for cross sections and polarization observables, respectively. At forward angles, the SCDW calculations reproduce the observed cross sections fairly well around the quasielastic peak. The one-step contribution is dominant at ${\ensuremath{\theta}}_{\mathrm{lab}}=30\ifmmode^\circ\else\textdegree\fi{},$ while the two- and three-step contributions become more important with increasing reaction angle. At backward angles the calculations underestimate the cross sections in the whole region, which indicates the significance of higher-step contributions. The ${D}_{\mathrm{NN}}$ values, which are sensitive to the effective nucleon-nucleon interaction in the nuclear medium, are close to those calculated with the G-matrix interaction parametrized by the Melbourne group.

Semiclassical distorted wave model analysis of the complete set of spin transfer coefficients for multistep direct ( p, nx) at 350 MeV

The semiclassical distorted wave (SCDW) model of multistep direct processes is extended to calculate the double differential inclusive cross section (DDX) and the complete set of spin transfer coefficients ( D ij ) at energies of 350–400 MeV, taking account of one- and two-step processes. The DDX for ( p, p′ x) on 40Ca at 392 MeV is calculated and compared with experimental data. The calculated D ij and the DDXs for ( p, nx) on 12C and 40Ca at 346 MeV for the emission angle of 22° are compared with the measured ones. Features of the calculated D ij , the contribution of two-step processes in particular, are discussed in terms of the comparison with those of the DDX. The calculated DDX and D ij are analyzed in terms of the choice of the bare NN force on which the effective interaction is based, the difference in the methods of the calculation of G matrices, and the in-medium modification of effective interactions.

Inclusive reaction40Ca(p,p′x)at an incident energy of 392 MeV

Emission-energy distributions were measured for the inclusive ${}^{40}\mathrm{Ca}{(p,p}^{\ensuremath{'}})$ reaction at an incident energy of 392 MeV and an angular range between 25\ifmmode^\circ\else\textdegree\fi{} and 120\ifmmode^\circ\else\textdegree\fi{}. A semiclassical distorted wave (SCDW) model gives a reasonably good description of the experimental data. The extent to which the observed yields are dominated by a two-particle rescattering emission contribution is estimated by a theoretical method that is known to describe experimental data for ${}^{40}\mathrm{Ca}{(p,p}^{\ensuremath{'}}{p}^{\ensuremath{''}})$ reasonably well. The energy distribution of the two-particle inclusive yield is found to agree well with the first-step contribution of the SCDW theory. Consequently this suggests strongly that the inclusive ${(p,p}^{\ensuremath{'}})$ yield at forward angles and high emission energy consists mostly of two high-energy nucleons emitted in the first step of the collision.

Semiclassical distorted wave model with Wigner transform of one-body density matrix

A semiclassical distorted wave (SCDW) model with realistic single particle wave functions in a finite range single particle potential is presented for multistep direct processes in nucleon inelastic scattering and charge exchange reactions to the continuum, making use of the Wigner transform of a one-body density matrix. The higher momentum components of target nucleons are properly taken into account in comparison with the previous SCDW model with a local density Fermi gas model. The new SCDW model still gives a simple closed-form expression for the cross section with no free adjustable parameter which allows a simple intuitive interpretation, just as in the previous SCDW model. This model is applied to the analyses of multistep direct processes of ${}^{90}\mathrm{Zr}{(p,p}^{\ensuremath{'}}x)$ reactions at incident energies of 80 and 160 MeV. The calculated double differential cross sections including up to three-step processes are compared with experimental data. The calculated cross sections at backward angles are larger than those given by the previous calculations, and the agreement with experimental data is much improved. Discussions on the mechanism of this improvement are given in terms of the momentum distribution of target nucleons.

Theoretical modification on semiclassical distorted wave model and its application to the study of spin observables

The semiclassical distorted wave (SCDW) model of nucleon inelastic and charge exchange scattering at intermediate energies is modified to take accurate account of off-the-energy-shell matrix elements of the in-medium $N\ensuremath{-}N$ interaction and explicit account of the exchange of colliding two nucleons, making use of the G matrix parametrized in coordinate representation. The effects of the modification on the double differential inclusive cross sections are discussed for the cases of ${(p,p}^{\ensuremath{'}}x)$ and (p,nx) reactions on ${}^{90}\mathrm{Zr}$ at 160 MeV. The modification enables the SCDW model to calculate spin observables. The depolarizations in ${}^{58}\mathrm{Ni}{(p,p}^{\ensuremath{'}}x)$ at 80 MeV and ${}^{90}\mathrm{Zr}{(p,p}^{\ensuremath{'}}x)$ and ${}^{90}\mathrm{Zr}(p,nx)$ at 160 MeV by one- and two-step processes are calculated, and the result for ${}^{58}\mathrm{Ni}{(p,p}^{\ensuremath{'}}x)$ is compared with experimental data. The calculated spin flips in ${(p,p}^{\ensuremath{'}}x)$ and (p,nx) on ${}^{90}\mathrm{Zr}$ are analyzed in terms of the effects of in-medium modification of the $N\ensuremath{-}N$ interaction and the contributions of individual components of the effective interaction.

Semiclassical distorted wave model analysis of multistep direct(p,p′x)and(p,nx)reactions to the continuum

The semiclassical distorted wave (SCDW) model is extended to include three-step process in multistep direct (MSD) processes in nucleon-induced preequilibrium nucleon-emission reactions. The extended SCDW model is applied to analyses of MSD processes in ${}^{58}\mathrm{Ni}{(p,p}^{\ensuremath{'}}{x),}^{90}\mathrm{Zr}{(p,p}^{\ensuremath{'}}{x),}^{90}\mathrm{Zr}(p,nx),$ and ${}^{209}\mathrm{Bi}{(p,p}^{\ensuremath{'}}x)$ in the incident energy range of 62--160 MeV. SCDW calculations with no adjustable parameter give overall good agreement with experimental double differential cross sections, except at very small and large angles. The nonlocality of distorting potentials is taken into account in terms of the Perey factor, and is found to be essential for reproducing the absolute magnitude of the cross sections. Effects of the density and momentum distributions of target nucleons and the use of in-medium $N\ensuremath{-}N$ cross sections on the SCDW calculation are discussed. Comparison with other models is made, in particular regarding the contributions of individual multistep processes to the calculated cross sections. Validity of the local semiclassical approximation to distorted waves, which is essential to SCDW is discussed on the basis of a numerical test.