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The precision of experimental data and analysis techniques is a key feature of any discovery attempt. A striking example is the proton radius puzzle where the accuracy of the spectroscopy of muonic atoms challenges traditional electron scattering measurements. The present work proposes a novel method for the determination of spatial moments from densities expressed in the momentum space. This method provides a direct access to even, odd, and more generally any real, negative and positive moment with order larger than $-3$. As an illustration, the application of this method to the electric form factor of the proton is discussed in detail.
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Photon strength, $f(E_{gamma})$, measured in photonuclear reactions, is the product of the average level density per MeV, $rho(E_x)$, and the average reduced level width, $Gamma_{gamma}/E_{gamma}^3$ for levels populated primarily by E1 transitions at an excitation energy $E_x=E_{gamma}$. It can be calculated with the Brink-Axel (BA) formulation modified to include contributions from the Giant Dipole Resonance (GDR) and higher lying resonances. Level densities and reduced widths have been calculated for 17 nuclei with atomic numbers between Z=14-92. Level densities below the GDR energy were calculated with the CT-JPI model and combined with the BA photon strength to determine the associated reduced widths. The reduced widths varied exponentially with level energy and could be extrapolated up to higher energies. The extrapolated widths were then combined with the BA photon strength to determine the level densities at higher energies. The level densities are found to increase exponentially at low energies, peak near the GDR energy due to the appearance of new states at the $2hbaromega$ shell closure, and continue to increase less rapidly up to at least 30 MeV. The average level densities have been compared with the Fermi Gas Level Density (FGLD), Back-Shifted Fermi Gas (BSFG), and Hartree-Fock-Bogoliubov (HFB) models. Good agreement is found with the nearly identical FGLD and BDFG models, while the HFB models gives substantially lower level densities. A universal set of FGLD model parameters were determined as a function of mass and temperature that are applicable to all nuclei.
We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly-magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLOsat chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for ${}^{100}$Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.
On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al.. De Rujulas idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.
We derive the free energy for fermions and bosons from fragmentation data. Inspired by the symmetry and pairing energy of the Weizsacker mass formula we obtain the free energy of fermions (nucleons) and bosons (alphas and deuterons) using Landaus free energy approach. We confirm previously obtained results for fermions and show that the free energy for alpha particles is negative and very close to the free energy for ideal Bose gases. Deuterons behave more similarly to fermions (positive free energy) rather than bosons. This is due to their low binding energy, which makes them very fragile, i.e., easily formed and destroyed. We show that the {alpha}-particle fraction is dominant at all temperatures and densities explored in this work. This is consistent with their negative free energy, which favors clusterization of nuclear matter into {alpha}-particles at subsaturation densities and finite temperatures. The role of finite open systems and Coulomb repulsion is addressed.
The static quadrupole moments (SQMs) of nuclear chiral doublet bands are investigated for the first time taking the particle-hole configuration $pi(1h_{11/2}) otimes u(1h_{11/2})^{-1}$ with triaxial deformation parameters in the range $260^circ leq gamma leq 270^circ$ as examples. The behavior of the SQM as a function of spin $I$ is illustrated by analyzing the components of the total angular momentum. It is found that in the region of chiral vibrations the SQMs of doublet bands are strongly varying with $I$, whereas in the region of static chirality the SQMs of doublet bands are almost constant. Hence, the measurement of SQMs provides a new criterion for distinguishing the modes of nuclear chirality. Moreover, in the high-spin region the SQMs can be approximated by an analytic formula with a proportionality to $cosgamma$ for both doublet bands. This provides a way to extract experimentally the triaxial deformation parameter $gamma$ for chiral bands from the measured SQMs.
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