The dependence of the nuclear charge form factor on short-range correlations and surface fluctuation effects

Abstract

We investigate the effects of fluctuations of the nuclear surface on the harmonic oscillator elastic charge form factor of light nuclei, while simultaneously approximating the short-range correlations through a Jastrow correlation factor. Inclusion of surface-fluctuation effects within this description, by truncating the cluster expansion at the two-body part, is found to improve somewhat the fit to the elastic charge form-factor of 16 O and 40 Ca. However, the convergence of the cluster expansion is expected to deteriorate. An additional finding is that the surface-fluctuation correlations produce a drastic change in the asymptotic behavior of the point-proton form factor, which now falls off quite slowly (i.e. as const. · q −4 ) at large values of the momentum transfer q.

Effects of Short and Long Range Correlations on the Charge Densities and Radii of Ca Nuclei

“…It is therefore the combination of SRC and SFC that gives the correct de scription of the density differences as well as of the charge form factors [10], while simultaneously the parabolic behavior of the charge radii is reproduced well. One could say that the putative roles of the mean-field, short range cor relations and surface fluctuation effects get mixed up to some degree.…”

“…It is also able to reproduce well the trend of the variation of the charge radii of Ca nuclei with the mass number. Moreover the model improves the description of the experimental charge form factors [10].…”

“…This was an indication that additional correlations were necessary to improve the agreement with the experiment. On the other hand, recently, the effect of fluctuations of the nuclear surface was also included in the model [10]. It was shown that the combined effects of SRC and of the surface fluctuation correlations (SFC) improved the description of the experimental charge form factors of 16 0 and ^Ca nuclei.…”

Evaluation of cluster expansions and correlated one-body properties of nuclei

“…It should be noted also that in these two exceptions the difference in the χ 2 values for the two expansions in both nuclei is less than 1%. Finally, we consider the so-called "healing" or "wound" integrals, denoted here as w 2 nl [37,41] for the various states of the relative two-nucleon motion, pertinent to the closed shell nuclei of Table I and in each case, that is in each of the cluster expansions FIY, FAHT and LOA. The values of these integrals express in a way the "amount of correlations" introduced to each state of the relative two-nucleon motion.…”

Μελέτη Των Παραγόντων Μορφής Και Της Κατανομής Της Ορμής Των Νουκλεονίων Σε Ελαφρούς Πυρήνες

“…98) οπού g(r, r 2 , z) = exp[-^(r 2 + r\)\ exp[2^rr 2 ] (3.99) Ο όρος ενός σώματος (O r )i, όπως εύκολα προκύπτει από τη σχέση (3.50) έχει τη μορφή (Ο,)ι = 4 Σ Vnl(2l + ν-τ-φ'ΜΦηΜ ni 4π (3.100) Ο όρος των δύο σωμάτων 0 22 (r,z), όπου ζ = /3,2/3, προκύπτει από τα διαγώνια στοιχεία του όρου 0 22 (r',r,gi) και συνεπώς θα είναι 0 22 (r,z) = Jg(r,r 2 ,z)[ps D (r)p SD (r 2 )-/>f D (r,r 2 )]dr 2 , ζ = β,2β (3.101) Επίσης, χρησιμοποιώντας τη σχέση (3.91) συμπεραίνουμε ότι ο όρος αυτός μπορεί να γραφεί με την κομψή μορφή 0 22 (r,z) = 4 Σ 7? n ,,,^, J (2/i + l)(2/ i + l) 71 ( ί t y it J ϊ J Κατά αντιστοιχεία με τον ΠΠ ο όρος 0 22 (r, ζ) για τους πυρήνες ls-lp και Id-2s φλοιών μπορεί να γραφεί ως συνάρτηση των στοιχείων Α™ 3^™4 ; 4 (r,z) ως εξής 0 22 (r,z) = 4 [ 3A°r°(r, zHs + [33<S'°(r, *) " 6<£' 2 (r, *)1 % 2 p + 3<°•°(Γ, ζ) + 12A--' u (r, ζ) -6-4^(r, r',s) (r, ζ) + 20Α°Ο^•°(Γ, ζ) -l(L« 2 (r,*) 4A^°'°(r, ζ) + 4A\Z'°(r, ζ) -2^g»'°(r, ζ)] *.%.…”