Expressions of the parallel and perpendicular temperature-dependent particle-number projected nuclear moment of inertia have been established by means of a discrete projection method. They generalize that of the FTBCS method and are well adapted to numerical computation. The effects of particle-number fluctuations have been numerically studied for some even-even actinide nuclei by using the single-particle energies and eigenstates of a deformed Woods-Saxon mean field. It has been shown that the parallel moment of inertia is practically not modified by the use of the projection method. In contrast, the discrepancy between the projected and FTBCS perpendicular moment of inertia values may reach 5%. Moreover, the particle-number fluctuation effects vary not only as a function of the temperature but also as a function of the deformation for a given temperature. This is not the case for the system energy.

Radiative corrections in the leading logarithmic approximation are calculated for the differential cross section of $e^{-}{\mu }^{+}$ radiative scattering. In particular the interference term due to photon emission from the electron and muon blocks are calculated in helicity independent and dependent parts. The calculation is applied to the kinematical conditions of existing deeply virtual Compton scattering (DVCS) data in electron-proton collisions. Both helicity odd and helicity even differential cross sections are considered.

In this paper, we develop a formalism for incorporating hadron loops into the quark model. We derive expressions for mass shifts, continuum components, and mixing amplitudes of “quenched” quark model states due to hadron loops, as perturbation series in the valence-continuum coupling Hamiltonian. We prove three general theorems regarding the effects of hadron loops, which show that given certain constraints on the external “bare” quark model states, the valence-continuum coupling, and the hadrons summed in the loops, the following results hold: (1) The loop mass shifts are identical for all states within a given $N,L$ multiplet. (2) These states have the same total open-flavor decay widths. (3) Loop-induced valence configuration mixing vanishes provided that $L_i\ne L_f$ or $S_i\ne S_f$. The charmonium system is used as a numerical case study, with the ${}^3{P}_0$ decay model providing the valence-continuum coupling. We evaluate the mass shifts and continuum mixing numerically for all $1S,1P$, and $2S$ charmonium valence states due to loops of $D,D^{*},D_s$, and $D_s^{*}$ meson pairs. We find that the mass shifts are quite large but numerically similar for all the low-lying charmonium states, as suggested by the first theorem. Thus, loop mass shifts may have been “hidden” in the valence quark model by a change of parameters. The two-meson continuum components of the physical charmonium states are also found to be large, creating challenges for the interpretation of the constituent quark model.

I study an aspect of chiral perturbation theory (χPT) that enables one to “bridge” different reactions. That is, an operator fixed in one of the reactions can then be used to predict the other. For this purpose, I calculate the partial-wave amplitude for the $p$-wave pion production ($\mathit{pp}\to \mathit{pn}{\pi }^{+}$) using the pion production operator from the lowest and the next nonvanishing orders. The operator includes a contact operator whose coupling has been fixed using a matrix element of a low-energy weak process ($\mathit{pp}\to {\mathit{de}}^{+}{\nu }_e$). I find that this operator does not reproduce the partial-wave amplitude extracted from experimental data, showing that the bridging over the reactions with significantly different kinematics is not necessarily successful. I study the dependence of the amplitude on the various inputs such as the $\mathit{NN}$ potential, the $\pi N\Delta$ coupling, and the cutoff. I argue the importance of a higher-order calculation. To gain an insight into a higher-order calculation, I add a higher-order counter term to the operator used above and fit the couplings to both the low-energy weak process and the pion production. The energy dependence of the partial-wave amplitude for the pion production is described by the operator consistently with the data. However, I find a result that tells us to be careful about the convergence of the chiral expansion for the $\mathit{pp}\to \mathit{pn}{\pi }^{+}$ reaction.

We show that the recently noted suppression of the fusion cross section induced by ${}^6\mathrm{He}$ nuclei at above-barrier energies compared to coupled channels calculations based on double-folding type potentials can be explained in part by coupling to the (${}^6\mathrm{He}$,${}^5\mathrm{He}$) single-neutron stripping reaction. We also show that these couplings have a significant effect on the near-barrier elastic scattering of ${}^6\mathrm{He}$ that should be included in any attempt at a complete description of this process.

Proton-neutron quasiparticle random phase approximation (pn-QRPA) theory has recently been used for the calculation of stellar weak interaction rates of the fp-shell nuclide with success. Neutrino losses from protoneutron stars play a pivotal role in deciding if these stars would be crushed into black holes or explode as supernovas. The product of abundance and positron capture rates on ${}^{55}\mathrm{Co}$ is substantial and as such can play a role in the fine tuning of input parameters of simulation codes especially in the presupernova evolution. Recently we introduced our calculation of capture rates on ${}^{55}\mathrm{Co}$, in a luxurious model space of $7\hslash \hspace{1em}\omega$, employing the pn-QRPA theory with a separable interaction. Simulators, however, may require these rates on a fine scale. Here we present for the first time an expanded calculation of the neutrino energy loss rates and positron capture rates on ${}^{55}\mathrm{Co}$ on an extensive temperature-density scale. This type of scale is appropriate for interpolation purposes and of greater utility for simulation codes. The pn-QRPA calculated neutrino energy loss rates are enhanced roughly up to two orders of magnitude compared with the large-scale shell model calculations and favor a lower entropy for the core of massive stars.

We report on a new lifetime measurement of the $E_x=6792$ keV state in ${}^{15}\mathrm{O}$ via the Doppler-shift attenuation method at the $E=259$ keV resonance in the reaction ${}^{14}\mathrm{N}$($p,\gamma$)${}^{15}\mathrm{O}$. This subthreshold state is of particular importance for the determination of the ground state astrophysical $S$ factor of ${}^{14}\mathrm{N}$($p,\gamma$)${}^{15}\mathrm{O}$ at stellar energies. The measurement technique has been significantly improved over that used in previous work. The conclusion of a finite lifetime drawn there cannot be confirmed with the present data. In addition, the lifetimes of the two states at $E_x=5181$ and 6172 keV have been measured with the same technique in order to verify the experimental method. We observe an attenuation factor $F(\tau )>0.98$ for the $E_x=6172$ and 6792 keV states, respectively, corresponding to $\tau <0.77$ fs. The attenuation factor for the $E_x=5181$ keV state results in $F(\tau )=0.78\pm 0.02$ corresponding to $\tau =8.4\pm 1.0$ fs, which is in excellent agreement with literature.

We explore the deformation properties of the newly postulated Barcelona-Catania-Paris (BCP) energy density functional (EDF). The results obtained for three isotope chains of Mg, Dy, and Ra are compared to the available experimental data as well as to the results of the Gogny-D1S force. Results for the fission barrier of ${}^{240}\mathrm{Pu}$ are also discussed.

Within a fully covariant model based on an effective Lagrangian picture, we investigate the hypernuclear production in a photon-nucleus interaction on an ${}^{16}\mathrm{O}$ target. The explicit kaon production vertex is described via creation, propagation, and decay into relevant channels of $N^{*}(1650)$, $N^{*}(1710)$, and $N^{*}(1720)$ intermediate baryonic resonance states in the initial interaction of the incident photon with one of the target protons. Bound state nucleon and hyperon wave functions are obtained by solving the Dirac equation. Using vertex parameters determined in the previous studies, contributions of the $N^{*}(1710)$ baryonic resonance dominate the total production cross sections which are found to peak at photon energies below 1 GeV. The results show that photoproduction is the most appropriate means for studying the unnatural parity hypernuclear states, thus accessing the spin dependence of the hyperon-nucleon interaction.

We present STAR results on the elliptic flow $v_2$ of charged hadrons, strange and multistrange particles from $\sqrt{s_{\mathit{NN}}}=200$ GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). The detailed study of the centrality dependence of $v_2$ over a broad transverse momentum range is presented. Comparisons of different analysis methods are made in order to estimate systematic uncertainties. To discuss the nonflow effect, we have performed the first analysis of $v_2$ with the Lee-Yang zero method for $K_S^0$ and Λ. In the relatively low $p_T$ region, $p_T⩽2\hspace{1em}\mathrm{GeV}/c$, a scaling with $m_T-m$ is observed for identified hadrons in each centrality bin studied. However, we do not observe $v_2(p_T)$ scaled by the participant eccentricity to be independent of centrality. At higher $p_T,2⩽p_T⩽6\hspace{1em}\mathrm{GeV}/c,v_2$ scales with quark number for all hadrons studied. For the multistrange hadron Ω, which does not suffer appreciable hadronic interactions, the values of $v_2$ are consistent with both $m_T-m$ scaling at low $p_T$ and number-of-quark scaling at intermediate $p_T$. As a function of collision centrality, an increase of $p_T$-integrated $v_2$ scaled by the participant eccentricity has been observed, indicating a stronger collective flow in more central Au+Au collisions.

The ambiguities and inconsistencies in previous thermodynamic treatments for the quark-mass density-dependent model are addressed. A new treatment is suggested to obtain self-consistent results. A new independent variable of effective mass is introduced to make the traditional thermodynamic calculation with partial derivatives still practicable. The contribution from physical vacuum has been discussed. We find that the properties of strange quark matter given by the quark-mass density-dependent model are nearly the same as those obtained by the MIT bag model after considering the contribution of the physical vacuum. Besides the quark system, according to our argument, the new independent variable of effective mass should be taken seriously in any thermodynamically consistent treatment whenever the medium effect is represented in the mass term.

In-beam γ-ray spectroscopy of ${}^{66,68}\mathrm{Fe}$ following intermediate-energy one- and two-proton knockout from cobalt and nickel secondary beams has been performed at the National Superconducting Cyclotron Laboratory. New transitions have been observed in ${}^{66}\mathrm{Fe}$ and ${}^{68}\mathrm{Fe}$. This is the first observation of γ-ray transitions in ${}^{68}\mathrm{Fe}$. In addition, ${}^{64}\mathrm{Cr}$ was produced using the ${}^9\mathrm{Be}$(${}^{66}\mathrm{Fe}$,${}^{64}\mathrm{Cr}$)X two-proton knockout reaction. An unexpectedly low inclusive cross section is observed for this reaction, an order of magnitude smaller than for the ${}^9\mathrm{Be}$(${}^{68}\mathrm{Ni}$,${}^{66}\mathrm{Fe}$)X reaction. This observation is discussed in terms of a significant structural difference between ${}^{66}\mathrm{Fe}$ and ${}^{64}\mathrm{Cr}$ and considerable admixtures of $\nu (\mathit{pf}){}^{n-2}(g_{9/2}){}^{+2}$ configurations in the ground and excited states of ${}^{64}\mathrm{Cr}$ at $N=40$.

The connections between the E(5) models [the original E(5) using an infinite square well, E(5)-${\beta }^4$, E(5)-${\beta }^6$, and E(5)-${\beta }^8$], based on particular solutions of the geometrical Bohr Hamiltonian with γ-unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the U(5)-O(6) transition line is used and a numerical fit to the different E(5) models energies is performed, later on the obtained wave functions are used to calculate $B(E2)$ transition rates. It is shown that within the IBM one can reproduce very well all these E(5) models. The agreement is the best for E(5)-${\beta }^4$ and reduces when passing through E(5)-${\beta }^6$, E(5)-${\beta }^8$, and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest-lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed.

Recently, we suggested that low-energy β-beam neutrinos can be very useful for the study of supernova-neutrino interactions. In this article, we examine the use of a such experiment for the analysis of a supernova-neutrino signal. Because supernova neutrinos are oscillating, it is very likely that the terrestrial spectrum of supernova neutrinos of a given flavor will not be the same as the energy distribution with which these neutrinos were first emitted. We demonstrate the efficacy of the proposed method for untangling multiple neutrino spectra. This is an essential feature of any model aiming at gaining information about the supernova mechanism, probing proto-neutron star physics, and understanding supernova nucleosynthesis, such as the neutrino process and the r-process. We also consider the efficacy of different experimental approaches including measurements at multiple beam energies and detector configurations.

A fission formalism which describes transmission and absorption through multiple humped barriers using a recursive method is proposed. Developed within the optical model for fission, it accounts for the fission mechanisms associated to the different degrees of damping of the vibrational states accommodated by the minima of the fission path. It can provide accurate description of experimental fission cross sections, including their resonant structure at low energies, and could be used in conjunction with global microscopic parameters in blind calculations of the fission process even for nuclei far from stability.

A Bethe-Salpeter-Faddeev (BSF) calculation is performed for the pentaquark ${\Theta }^{+}$ in the diquark picture of Jaffe and Wilczek in which ${\Theta }^{+}$ is a diquark-diquark-$\overline{s}$ three-body system. The Nambu–Jona-Lasinio (NJL) model is used to calculate the lowest order diagrams in the two-body scatterings of $\overline{s}D$ and $DD$. With the use of coupling constants determined from the meson sector, we find that $\overline{s}D$ interaction is attractive in $s$-wave while the $\mathit{DD}$ interaction is repulsive in the $p$-wave. With only the lowest three-body channel considered, we do not find a bound ${\frac{1}{2}}^{+}$ pentaquark state. Instead, a bound pentaquark ${\Theta }^{+}$ with ${\frac{1}{2}}^{-}$ is obtained with unphysically strong vector mesonic coupling constants.

The fusion-evaporation reaction ${}^9\mathrm{Be}$(${}^{11}\mathrm{B}$,$2p$) was used to populate excited states in ${}^{18}\mathrm{N}$. New gamma-ray transitions were added to the ${}^{18}\mathrm{N}$ level scheme. The mean lifetime of the first excited state was measured to be 582(165) ps and its transition rate to the ground state was determined to be $B(M1)=0.036(10)$ W.u. Shell model calculations in the full $p\text{−}\mathit{sd}$ model space were used to investigate the low-lying configurations in ${}^{18}\mathrm{N}$ and in the $N=11$ isotones ${}^{17}\mathrm{C}$ and ${}^{19}\mathrm{O}$. It was found that the role of the proton-neutron interaction is important in determining the ground state and low-lying excited state properties. The ground state spin inversion in these isotones is attributed to the increased importance of the quadrupole relative to the pairing interaction and is discussed within the framework of a schematic pairing + quadrupole model.

The bound kaon approach to the strangeness in the Skyrme model is applied to investigating the possibility of deeply bound $K^{-}\mathit{pp}$ states. We describe the $K^{-}\mathit{pp}$ system as two Skyrmion, around which a kaon field fluctuates. Each Skyrmion is rotated in the space of SU(2) collective coordinate. The rotational motions are quantized to be projected onto the spin-singlet proton-proton state. We derive the equation of motion for the kaon in the background field of two Skyrmions at fixed positions. From the numerical solution of the equation of motion, it is found that the energy of $K^{-}$ can be considerably small and that the distribution of $K^{-}$ shows molecular nature of the $K^{-}\mathit{pp}$ system. For this deep binding, the Wess-Zumino-Witten term plays an important role. The total energy of the $K^{-}\mathit{pp}$ system is estimated in the Born-Oppenheimer approximation. The binding energy of the $K^{-}\mathit{pp}$ state is B.E. $\simeq 126$ MeV. The mean square radius of the $\mathit{pp}$ subsystem is $\sqrt{\langle r_{\mathit{pp}}^2\rangle }\simeq 1.6$ fm.

The reaction ${}^{24}\mathrm{Mg}$($\alpha ,\gamma$)${}^{28}\mathrm{Si}$ is involved in the nucleosynthesis of ${}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}$ in massive stars. The reaction has not been examined with sufficient sensitivity at α-particle energies below 1.5 MeV. Several ${}^{28}\mathrm{Si}$ states appear favorable for formation by this reaction in the α-particle energy range of 1.0–1.5 MeV, motivating a new study of this reaction at the University of Notre Dame. To maximize experimental sensitivity, a high efficiency coincidence detection system was developed. Several previously unknown resonances were observed between 1.1 and 1.5 MeV, and an upper limit for any lower energy resonances was obtained. Resonance parameters were determined and reaction rates were calculated. The astrophysical implications of these results are discussed.

Two-quasiparticle states in ${}^{250}\mathrm{Bk}$ were investigated with decay scheme studies and the single-neutron transfer reaction ${}^{249}\mathrm{Bk}$($d,p$)${}^{250}\mathrm{Bk}$. Mass-separated sources of ${}^{254}\mathrm{Es}$ were used for α singles and $\alpha \text{−}\gamma$ coincidence measurements. These studies, plus previous studies of ${}^{254}{\mathrm{Es}}^m$ α decay and the ${}^{249}\mathrm{Bk}$($n,\gamma$) reaction, provide spins and parities of the observed levels. The transfer reaction ${}^{249}\mathrm{Bk}$($d,p$)${}^{250}\mathrm{Bk}$ was used to deduce neutron single-particle components of the observed bands. Six pairs of singlet and triplet states, formed by the coupling of proton and neutron one-quasiparticle states, were identified. The splitting energies between the triplet and singlet states were found to be in agreement with previous calculations.