Independent-Particle Model and the Nuclear Photoeffect. II

Abstract

A simple harmonic oscillator independent-particle model is used for sum-rule calculation of electric dipole transitions in the nuclear photoeffect. First we find the level spacing hco = 4:2A~i Mev for nuclear radius parameter ro=1.2. Combining this result with the integrated cross section, we find the bremsstrahlungweighted cross section cb~f(<r/W)dW = 0.36^4 4/3 millibarns. The calculated OT> is not inconsistent with a preliminary analysis of experimental measurements for He, Be, C, Al, Cu, Mo, Ag, Ta, Pb, and U. We also use the simple harmonic oscillator independent-particle model to calculate the increase in the integrated cross section due to neutron-proton exchange forces. We find that the relative increase is not far from the Levinger-Bethe value of 0.8x (where x is the fraction of exchange force) for the closed-shell nuclei He 4 , O 16 , and Ca 40 , for both Gaussian and Yukawa neutron-proton potentials, and for two values of the radius parameter ro: 1.2 or 1.5.

Nuclear Photo-Reaction and Excitation Modes of Nuclei

“…(5) and (9) . It indicates a very sharp peak at 14 Mev with the ;m,r=15 mb-Mev. * It seems to be unaccountable at a glance that this peak is by far sharper than the peak seen in the r-reaction 'of C l3 or N 14 • In F l9 Cr, n) F ls , however, the peak consists of the nuclear excitation from the d 5 / 2 state to the f; /2 state.…”

“…The giant resonance and the core excitation mode As we referred in § 1, the giant resonance is essentially due to the core excitation and its, resonance energy for the various nuclei is much higher than the prediction by the independent particle model so far as the nuclear potential is assumed to be velocity-independent. The above matter can be understood easily in the speeial case that the nuclear potential is of harmonie oseillator: (14) Then, Brink 13 ) indicated that the Hamiltonian can be transformed as follows, (16) S. Fujii i and j mean the i-th proton and the j-th neutron respectively, and Hillt is quite independent of the centre of mass and the dipole vibration coordinates. From the above equations Brink pointed out that the Goldhaber-Teller collective mode is contained alreadly within the shell model description.…”

Dynamical Correlations and the Nuclear Photoeffect

“…To be definite, we have taken the upper limits of the relevant C's (see Table IV). Results for the O"' quantities at r = 5 fm-1 (ranging over the same set of A's as in § 6) are collected in Tables VIII and IX, while Table X displays the corresponding W values. Our C 1 results for the Fermi-gas model are compared with those for the dynamically correlated model at r = 5 fm-1 in Table XI.…”