Reaction cross section calculations for deformed nuclei

Abstract

Optical limit Glauber theory calculations of reaction cross sections, used to deduce nuclear sizes from high energy data, are studied in the case of a deformed projectile ͑or target͒. We show that a previously applied formula, used to adjust the root-mean-squared radius deduced assuming spherical projectiles, is consistent with results which treat the projectile deformation explicitly within the reaction calculation. The correct interpretation of this formula in studies of reaction cross sections is clarified. ͓S0556-2813͑99͒04304-6͔ PACS number͑s͒: 21.10. Gv, 11.80.Fv, 25.10.ϩs, 27.20.ϩn The optical limit ͑OL͒ approximation to Glauber theory ͓1,2͔ has been used frequently in analyses to extract empirical root-mean-squared ͑rms͒ matter radii of nuclei from intermediate energy reaction and interaction cross section measurements ͓3-5͔. The inputs to this model are the projectile and target nucleus one-body densities. Their geometric overlap at a given impact parameter, when multiplied by an appropriate nucleon-nucleon (NN) reaction cross section, determines the calculated projectile-target reaction cross section. This is then compared with the measurements. This approach works very well for localized nuclei where nucleons occupy a well-defined volume ͓3͔. For nuclei with weakly bound and delocalized nucleons, recent theoretical analyses ͓6-8͔ have shown that projectile excitation and breakup effects are important. Then a more explicit fewbody treatment is necessary for quantitative calculations of the reaction cross sections. This weak binding effect alters ͑increases͒ the transparency of the collision at larger impact parameters, reducing the reaction cross section for a given projectile rms size.Our interest here is the reaction cross section of an assumed localized quadrupole-deformed projectile with deformation parameter ␤. At high energy, in the sudden or adiabatic approximation limit, and in a given collision, the deformed projectile nucleus will traverse the target nucleus with a fixed orientation ⍀ ͑Fig. 1͒. The transparency of the collision and cross section for a given ⍀ will depend sensitively on this projectile orientation, particularly for neargrazing-impact parameters b. The physical cross section, for an assumed unpolarized incident projectile beam, is then the average of such cross sections over all orientations ͓9͔.To date, even when the projectile nuclei are deformed, OL reaction calculations have been carried out for spherical densities, e.g., ͓10,11͔. For nuclei with quadrupole deformation ␤, the effects of deformation were then discussed using the mean-squared radius formula ͑1͒carried over from other applications, such as the analysis of energy shifts in muonic atom data ͓12͔, where the nuclear density is also required. In Ref. ͓11͔, ͗r 2 ͘ ␤ was interpreted as the mean-squared radius of the deformed projectile deduced directly from cross section data using a spherical density OL reaction calculation. Equation ͑1͒ was then used to subtract the effects of the projectile deformation through ...

Dynamical core deformation effects on single-nucleon knockout reactions at fragmentation beam energies

“…This view was supported by an estimate of the effects on the stripping cross section [5]. Conversely, an earlier estimate was made of collective, core rotational excitation in the case of neutron knockout from 11 Be [6], where a contribution from 0 + → 2 + state inelastic excitation of 10 Be was significant and was needed to explain an enhanced 10 Be(2 + ) final state partial cross section. There the changes were anticipated as arising principally from an enhanced elastic breakup component.…”

“…The application of this frozen-orientation approximation to calculations of the more restricted problem, of deformed coretarget elastic and inelastic scattering and to calculations of reaction cross sections, can be found in Refs. [10,11].…”

“…In the case of a quadrupole deformed core of density ρ c (r, ) interacting with a spherical target of density ρ t (r) then (29) where (e.g., Ref. [11]):…”

“…Following Ref. [11] the phase entering the core S matrix can be expressed as a Legendre polynomial expansion…”

“…III the treatment of the core-and nucleon-target S matrices. Section IV then presents the model results for applications to neutron knockout reactions from 11 Be and 17 C secondary beams on a 9 Be target. Section V contains our concluding remarks.…”