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Register a new userRelation between (e,e) sum rules in 6,7Li and 4He nuclei.Experiment and cluster model
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The sums over (e,e) spectra of 6Li and 7Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the alpha-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm^{-1} the relations expressing the A=6 or 7 sum in terms of the A=4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm^{-1} the longitudinal correlation functions of 6Li and 7Li nuclei are found to be close to that of the alpha-particle. The experimental longitudinal sums in the range between 0.450 and 1.625 fm^{-1} are employed to perform comparison with those calculated in the framework of cluster models. Out of the mentioned experimental sums, those in the range between 0.750 and 1.000 fm^{-1} in the 6Li case and between 0.750 and 1.125 fm^{-1} in the 7Li case are obtained in the present work. In the 6Li case a complete agreement is found while in the 7Li case an agreement only at a qualitative level is observed.
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After recapitulating the procedure to find the bands and the states occurring in the $mathcal{D}_{3h}$ alpha-cluster model of $^{12}$C in which the clusters are placed at the vertexes of an equilateral triangle, we obtain the selection rules for electromagnetic transitions. While the alpha cluster structure leads to the cancellation of E1 transitions, the approximations carried out in deriving the roto-vibrational hamiltonian lead to the disappearance of M1 transitions. Furthermore, although in general the lowest active modes are E2, E3, $cdots$ and M2, M3, $cdots$, the cancellation of M2, M3 and M5 transitions between certain bands also occurs, as a result of the application of group theoretical techniques drawn from molecular physics. These implications can be very relevant for the spectroscopic analysis of $gamma$-ray spectra of $^{12}$C.
Lowest order and higher order QED calculations have been carried out for the RHIC high mass e+ e- pairs observed by PHENIX with single ZDC triggers. The lowest order QED results for the experimental acceptance are about two standard deviations larger than the PHENIX data. Corresponding higher order QED calculations are within one standard deviation of the data.
A new lowest order QED calculation for RHIC e+ e- pair production has been carried out with a phenomenological treatment of the Coulomb dissociation of the heavy ion nuclei observed in the STAR ZDC triggers. The lowest order QED result for the experimental acceptance is nearly two standard deviations larger than the STAR data. A corresponding higher order QED calculation is consistent with the data.
The correction to the Coulomb energy due to virtual production of $e^+e^-$ pairs, which is on the order of one percent of the Coulomb energy at nuclear scales is discussed. The effects of including a pair-production term in the semi-empirical mass formula and the correction to the Coulomb barrier for a handful of nuclear collisions using the Bass and Coulomb potentials are studied. With an eye toward future work using Constrained Molecular Dynamics (CoMD) model, we also calculate the correction to the Coulomb energy and force between protons after folding with a Gaussian spatial distribution.
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