We use effective field theory (EFT) to calculate the nucleon-nucleon scattering amplitude up to next-to-next-to-leading order (NNLO), where we include instantaneous pion exchange but ignore retardation effects. The scattering amplitude in the ${}^1{S}_0$ channel is calculated using the Kaplan-Savage-Wise power counting scheme. An expansion of the amplitude about the pole at low (imaginary) momentum is used to derive matching conditions for the EFT couplings. After imposing constraints from a renormalization group flow analysis, there are no new free parameters in the amplitude at NNLO. We apply the calculation to a toy model in which there is only instantaneous pion exchange by construction, namely, the two-Yukawa model. We find that, through next-to-next-to-leading order, each successive term in the low energy expansion does systematically improve the approximation to the full amplitude.

States in ${}^{162}\mathrm{Dy}$ populated in the $\beta$ decay of ${}^{162}\mathrm{Ho},$ produced in the ${}^{159}\mathrm{Tb}(\alpha ,n)$ reaction, were studied with high efficiency Ge detectors with the aim of assessing a possible candidate for a $K^{\pi }{=0\mathrm{}}^{+}\gamma \gamma$ double phonon excitation near 1400 keV. Previous evidence in favor of such an interpretation is shown to be incorrect, while new data reestablishes the possibility of such a structure.

Using the particle-vibration coupling for particles moving in the harmonic oscillator potential, the anharmonicity in two-phonon states of monopole, dipole, and quadrupole giant resonances of shape vibrations is studied. The anharmonic term in both the energy and strength of two-phonon giant resonances vanishes in the leading order of $N_F\gg 1.$ Thus, instead of $A^{-1},$ the calculated energy shift becomes the order of $A^{-4/3},$ which is still the order of $A^{1/3}$ larger than that obtained from a macroscopic description of the vibrations.

If the antiproton optical potential includes the spin orbit interaction term, the $A(\overline{p},p^{\prime }{)A}^{*}$ inelastic scattering not only can excite the normal parity states, but also can excite the abnormal parity states. It also induces a polarization $P_f\left(\theta \right)$ at the inelastic scattering. In the framework of DWIA, we derive and calculate the inelastic scattering cross section and $P_f\left(\theta \right)$ for the ${}^{12}\mathrm{C}(\overline{p},p^{\prime }{)}^{12}{\mathrm{C}}^{*}$ with $2^{+},$ $3^{-},$ and $1^{+}$ states at antiproton energies of 46.8 and 179.7 MeV. Our model fit well the available experimental data. The 46.8 MeV measurement of the inelastic differential cross section to the $1^{+}$ abnormal parity state can be explained by a spin orbit term. Such a term generates a sizable inelastic scattering polarization.

The present knowledge about hadrons produced in relativistic heavy ion collisions is compatible with chemical freeze-out happening when the energy density divided by the particle density reaches the value of 1 GeV. This observation is used to determine the energy dependence of the chemical freeze-out parameters $T_{\mathrm{ch}}$ and ${\mu }_B^{\mathrm{ch}}$ for beam energies varying between 1 and $200A$ GeV. The consequences of this energy dependence are studied for various particle ratios. Predictions for particle ratios at beam energy $40A$ GeV are presented. The conditions for thermal freeze-out are also determined. These correspond either to an energy density of 45 ${\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{f}\mathrm{m}}^3$ or to a particle density of $0.05/{\mathrm{fm}}^3.$

Parity nonconservation (PNC) has been studied in the neutron p-wave resonances of ${}^{106}\mathrm{Pd}$ and ${}^{108}\mathrm{Pd}$ in the energy range of 20 to 2000 eV. Longitudinal asymmetries in p-wave capture cross sections are measured using longitudinally polarized neutrons incident on $\sim 20-\mathrm{g}$ metal-powder targets at LANSCE. A CsI $\gamma$-ray detector array measures capture cross section asymmetries as a function of neutron energy which is determined by the neutron time-of-flight method. A total of 21 p-wave resonances in ${}^{106}\mathrm{Pd}$ and 21 p-wave resonances in ${}^{108}\mathrm{Pd}$ were studied. One statistically significant PNC effect was observed in ${}^{106}\mathrm{Pd},$ and no effects were observed in ${}^{108}\mathrm{Pd}.$ For ${}^{106}\mathrm{Pd}$ a weak spreading width of ${\Gamma }_w{=34\mathrm{}}_{-28}^{+47\mathrm{}}\times {10}^{-7}\hspace{0.5em}\mathrm{eV}$ was obtained. For ${}^{108}\mathrm{Pd}$ an upper limit on the weak spreading width of ${\Gamma }_w<12\mathrm{}\times {10}^{-7}\hspace{0.5em}\mathrm{eV}$ was determined at the 68% confidence level.

In the single j shell there is a two to one relationship between the spectra of certain even-even and neighboring odd mass nuclei; e.g., the calculated energy levels of ${J=0\mathrm{}}^{+}$ states in ${}^{44}\mathrm{Ti}$ are at twice the energies of corresponding levels in ${}^{43}\mathrm{Ti}{(}^{43}\mathrm{Sc})$ with $J=j=7/2.\mathrm{}$ Here an approximate extension of the relationship is made by adopting a truncated seniority scheme; i.e., for ${}^{46}\mathrm{Ti}$ and ${}^{45}\mathrm{Sc}$ we get the relationship if we do not allow the seniority $v=4\mathrm{}$ states to mix with the $v=0\mathrm{}$ and $v=2\mathrm{}$ states. Better than that, we get very close to the two to one relationship if seniority $v=4\mathrm{}$ states are admixed perturbatively. In addition, it is shown that for the $J=0\mathrm{}\hspace{0.5em}T=3\mathrm{}$ state in ${}^{46}\mathrm{Ti}$ and for the $J=j\hspace{0.5em}T=5/2\mathrm{}$ state in ${}^{45}\mathrm{Sc}$ (i.e., the states of higher isospin) there are no admixtures in which the neutrons have seniority 4.

An exact approach for the determination of proton-decay widths in spherical nuclei is presented. It consists of solving numerically the one-dimensional time-dependent Schrödinger equation for initial proton quasistationary states obtained in the framework of a single-particle model. From the time dependence of the metastable state one can infer the dynamics of the decay and calculate the lifetime. The validity of this approach is demonstrated and quantitative comparisons with existing approximate, stationary methods are reviewed. Finally, the advantages and perspectives of this new method are discussed.

We report a model-independent partial-wave analysis of polarized $\mathrm{dd}$ fusion reactions at low energies. The radial transition amplitudes, designated by the central, spin-orbit, and tensor forces, are determined by fitting angular distributions of the tensor and vector analyzing powers $A_{\mathrm{XZ}}\left(\theta \right),$ $A_{\mathrm{ZZ}}\left(\theta \right),$ $A_{\mathrm{XX}-\mathrm{YY}}\left(\theta \right),$ and $A_Y\left(\theta \right),$ and the unpolarized cross section ${\sigma }_0\left(\theta \right).\mathrm{}$ The polarized fusion cross section ${\sigma }_{1,1}\left(\theta \right)$ is then predicted from these radial transition amplitudes. We stress that this is feasible only when these amplitudes are separated according to the tensor rank of the interaction. This study includes the D-state components of the deuteron, triton, and ${}^3\mathrm{He},$ and the partial-wave expansion is done up to the d wave for both the entrance and exit channels. Experimental data at $E_{\mathrm{lab}}=30,$ 50, 70, and 90 keV for the $d(d,p)t$ reaction are very well fitted with this method. It is found that the ratio of polarized to unpolarized cross sections is about 86% at 30 keV and goes down to 22% at 90 keV. The implication of the suppression of a polarized $\mathrm{dd}$ fusion reaction is discussed in the context of the neutron-lean fusion reactor with polarized D-${}^3\mathrm{He}$ fuel. It turns out that the important range of energy for suppressing the $d(d,p)t$ and ${d(d,n)\mathrm{}}^3\mathrm{He}$ reactions at the plasma temperature $T=60\mathrm{}$ keV is $E_d=80\mathrm{}$–600 keV. More experimental data are needed in this range to make a detailed study of the neutron suppression.

The contributions to the reaction cross section from elastic and inelastic breakup processes, calculated within the post-form distorted-wave Born-approximation theory, are used as constraints to determine the contributions to the imaginary part of the deuteron optical potential (IPDOP) due to the breakup channels. The Coulomb part of this potential due to the elastic breakup process is seen to account for the long range absorption in the optical potential. The nuclear parts of the IPDOP due to the elastic and inelastic breakup modes peak in different regions of the nuclear surface, with the latter being almost an order of magnitude larger than the former. This makes the IPDOP, due to the breakup channels determined by us, stronger than those calculated earlier ignoring the inelastic breakup mode.

An exactly solvable model is developed for multifragmentation which is an extension of an earlier model, to two-component systems. The model is quite versatile. One can use experimental binding energies and excited states of clusters as inputs to the model and compute, rather easily, many observables. In this paper we pay particular attention to specific heats (hence the caloric curves) of certain target projectile combinations. In idealized cases without Coulomb interactions, large systems show signatures of a first order phase transition. The caloric curves change significantly when Coulomb energy is included.

Multifragment emission following ${}^{129}\mathrm{Xe}{+}^{197}\mathrm{Au}$ collisions at $30A,$ $40A,$ $50A,$ and $60A\hspace{0.5em}\mathrm{MeV}$ has been studied with multidetector systems covering nearly $4\pi$ in solid angle. The correlations of both the intermediate mass fragment and light charged particle multiplicities with the transverse energy are explored. A comparison is made with results from a similar system ${}^{136}\mathrm{Xe}{+}^{209}\mathrm{Bi}$ at $28A\hspace{0.5em}\mathrm{MeV}.$ The experimental trends are compared to statistical model predictions.

A light-front treatment for finite nuclei is developed from a relativistic effective Lagrangian (QHD1) involving nucleons, scalar mesons, and vector mesons. We show that the necessary variational principle is a constrained one which fixes the expectation value of the total momentum operator $P^{+}$ to be the same as that for $P^{-}.$ This is the same as minimizing the sum of the total momentum operators: $P^{-}{+P}^{+}.$ We obtain a new light-front version of the equation that defines the single nucleon modes. The solutions of this equation are approximately a nontrivial phase factor times certain solutions of the usual equal-time Dirac equation. The ground-state wave function is treated as a meson-nucleon Fock state, and the meson fields are treated as expectation values of field operators in that ground state. The resulting equations for these expectation values are shown to be closely related to the usual meson field equations. A new numerical technique to solve the self-consistent field equations is introduced and applied to ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}.$ The computed binding energies are essentially the same as for the usual equal-time theory. The nucleon plus momentum distribution (probability for a nucleon to have a given value of $p^{+})$ is obtained, and peaks for values of $p^{+}$ about 70 percent of the nucleon mass. The mesonic component of the ground-state wave function is used to determine the scalar and vector meson momentum distribution functions, with a result that the vector mesons carry about 30 percent of the nuclear plus-momentum. The vector meson momentum distribution becomes more concentrated at $p^{+}=0\mathrm{}$ as A increases.

The $\pi \mathrm{NN}$ vertex function is calculated within a dispersion theoretical approach, including both $\pi \rho$ and $\pi \sigma$ intermediate states, where the $\sigma$ meson is an abbreviation for a correlated pion pair in a relative S wave with isospin $I=0\mathrm{}$. A strong coupling between the $\pi \sigma$ and $\pi \rho$ states is found. This leads to a softening of the $\pi \mathrm{NN}$ form factor. In a monopole parametrization, a cutoff $\Lambda \approx 800\mathrm{MeV}$ is obtained as compared to $\Lambda \approx 1000\mathrm{MeV}$ using $\pi \rho$ intermediate states only.

Experimental results are presented for the $\mathrm{pp}$ elastic-scattering single spin observable $A_{\mathrm{oono}}{=A}_{\mathrm{ooon}}{=A}_N=P,$ or the analyzing power, at 19 beam kinetic energies between 1795 and 2235 MeV. The typical c.m. angular range is $60–100°.$ The measurements were performed at Saturne II with a vertically polarized beam and target (transverse to the beam direction and scattering plane), a magnetic spectrometer and a recoil detector, both instrumented with multiwire proportional chambers, and beam polarimeters.

Measurements at 18 beam kinetic energies between 1975 and 2795 MeV and at 795 MeV are reported for the $\mathrm{pp}$ elastic-scattering single spin parameter $A_{\mathrm{ooon}}{=A}_{\mathrm{oono}}{=A}_N=P.\mathrm{}$ The c.m. angular range is typically $60–100°.$ These results are compared to previous data from Saturne II and other accelerators. A search for energy-dependent structure at fixed c.m. angles is performed, but no rapid changes are observed.

A $K^{\pi }{=8\mathrm{}}^{-}$ strongly coupled rotational band, which is built upon a 23 ns isomeric state, has been established in ${}^{170}\mathrm{Hf}.$ The single-particle configuration of the band has been determined from the in-band to out-of-band branching ratios and associated $|{(g}_K-g_R)|{/Q}_0$ values. The $\gamma$-ray decay of the $K^{\pi }{=8\mathrm{}}^{-}$ isomeric state proceeds through a $K^{\pi }{=6\mathrm{}}^{+}$ intrinsic state, in accordance with the K-selection rule. A complex array of delayed $\gamma$-ray transitions have been observed to link this $K^{\pi }{=6\mathrm{}}^{+},$ intrinsic bandhead state into the yrast states. In particular, a new $\Delta K=8,$ 1141 keV, $E1\mathrm{}$ transition links the $K^{\pi }{=8\mathrm{}}^{-}$ isomeric state directly to the ground-state band. The $\gamma$-ray reduced hindrance factor for this $E1\mathrm{}$ decay in ${}^{170}\mathrm{Hf}$ is the smallest $\Delta K=8\mathrm{}$ transition observed in the Hf nuclei. However, its value is consistent with that expected on the basis of the increased Coriolis mixing which occurs in the lighter Hf isotopes.

We study the ${}^{56}\mathrm{Fe}({\nu }_e{,e}^{-}{)}^{56}\mathrm{Co}$ cross section for the KARMEN neutrino spectrum. The Gamow-Teller contribution to the cross section is calculated within the shell model, while the forbidden transitions are evaluated within the continuum random phase approximation. We find a total cross section of $2.73\times {10}^{-40}{\mathrm{cm}}^2,$ in agreement with the data.

Shell model calculations are carried out for the spectra of nuclei with $92<~A<~98$ in the model space in which the valence protons occupy the ${1f}_{5/2},$ ${2p}_{3/2},$ ${2p}_{1/2},$ and ${1g}_{9/2}$ orbitals, and valence neutrons occupy ${1g}_{9/2},$ ${2p}_{1/2},$ ${2d}_{5/2},$ ${2d}_{3/2},$ ${3s}_{1/2},$ and ${1g}_{7/2}$ orbitals using a partition truncation method. We first select partitions that are big enough to describe the spectra of nuclei with $N=50.\mathrm{}$ Then we combine all possible valence neutron partitions with the selected valence proton partitions of the corresponding nuclei with $N=50\mathrm{}$ to diagonalize the Hamiltonians for the nuclei with $54>~N>~51.$ The weak-coupling scheme is used to analyze the experimental data and the calculated results. The concepts of independent nucleon-pair motion in even-even nuclei and the homologous state structure in even-odd nuclei are held in this mass region. The spectra of ${}_{42}^{95}{\mathrm{Mo}}_{53}$ and ${}_{43}^{95}{\mathrm{Tc}}_{52}$ share a special similar structure; i.e., the low-lying states of ${}_{42}^{95}{\mathrm{Mo}}_{53}$ up to 2.5 MeV can be obtained by replacing the last odd proton in ${}_{43}^{95}{\mathrm{Tc}}_{52}$ and vice versa.

The effects of the variation of vector meson masses and decay widths on photon production from hot and dense strongly interacting matter formed after $\mathrm{S}+\mathrm{Au}$ collisions at CERN Super Proton Synchrotron (SPS) energies are considered. It has been shown that the photon spectra measured by the WA80 Collaboration cannot distinguish between the formation of quark matter and hadronic matter in the initial state. The photon yield in $\mathrm{Pb}+\mathrm{Pb}$ collisions at CERN SPS and BNL Relativistic Heavy Ion Collider energies is estimated.