Tunable-fidelity wave functions for the \textit{ab initio} description of scattering and reactions

The no-core shell model (NCSM) is an \textit{ab initio} method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an \textit{ab initio} treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass $A\lesssim 16$ nuclei, except for variants where the basis is further down-selected via some truncation scheme. We consider a basis selection method for the NCSM that captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling \textit{ab initio} reaction calculations in $sd$-shell nuclei. The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). We present calculations for $^7$Li and $n+^{12}$C scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from $^{24}$Mg.Comment: 13 pages, 8 figure

Intruder configurations of excited states in the neutron-rich isotopes 33P and 34P

Excited states in the neutron-rich isotopes P33 and P34 were populated by the O18+O18 fusion-evaporation reaction at Elab=24 MeV. The Gammasphere array was used along with the Microball particle detector array to detect γ transitions in coincidence with the charged particles emitted from the compound nucleus S36. The use of Microball enabled the selection of the proton emission channel. It also helped in determining the exact position and energy of the emitted proton; this was later employed in kinematic Doppler corrections. 16 new transitions and 13 new states were observed in P33 and 21 γ rays and 20 energy levels were observed in P34 for the first time. The nearly 4π geometry of Gammasphere allowed the measurement of γ-ray angular distributions leading to spin assignments for many states. The experimental observations for both isotopes were interpreted with the help of shell-model calculations using the (0+1)ω PSDPF interaction. The calculations accounted for both the 0p-0h and 1p-1h states reasonably well and indicated that 2p-2h excitations might dominate the higher-spin configurations in both P33 and P34

Impact of the 6^6Li asymptotic normalization constant onto α\alpha-induced reactions of astrophysical interest

Indirect methods have become the predominant approach in experimental nuclear astrophysics for studying several low-energy nuclear reactions occurring in stars, as direct measurements of many of these relevant reactions are rendered infeasible due to their low reaction probability. Such indirect methods, however, require theoretical input that in turn can have significant poorly-quantified uncertainties, which can then be propagated to the reaction rates and have a large effect on our quantitative understanding of stellar evolution and nucleosynthesis processes. We present two such examples involving $\alpha$-induced reactions, $^{13}$C($\alpha,n)^{16}$O and $^{12}$C$(\alpha,\gamma)^{16}$O, for which the low-energy cross sections have been constrained with $(^6$Li$,d)$ transfer data. In this Letter, we discuss how a first-principle calculation of $^6$Li leads to a 21% reduction of the $^{12}$C$(\alpha,\gamma)^{16}$O cross sections with respect to a previous estimation. This calculation further resolves the discrepancy between recent measurements of the $^{13}$C$(\alpha,n)^{16}$O reaction and points to the need for improved theoretical formulations of nuclear reactions.Comment: 6 pages (including references) and 3 figure

Cross-shell excitations in Si 31

The Si31 nucleus was produced through the O18(O18, αn) fusion-evaporation reaction at Elab=24MeV. Evaporated α particles from the reaction were detected and identified in the Microball detector array for channel selection. Multiple γ-ray coincidence events were detected in Gammasphere. The energy and angle information for the α particles was used to determine the Si31 recoil kinematics on an event-by-event basis for a more accurate Doppler correction. A total of 22 new states and 52 new γ transitions were observed, including 14 from states above the neutron separation energy. The positive-parity states predicted by the shell-model calculations in the sd model space agree well with experiment. The negative-parity states were compared with shell-model calculations in the psdpf model space with some variations in the N=20 shell gap. The best agreement was found with a shell gap intermediate between that originally used for A≈20 nuclei and that previously adapted for P32,34. This variation suggests the need for a more universal cross-shell interaction

Evolution of the N=20 and 28 Shell Gaps and 2-particle-2-hole states in the FSU Interaction

The FSU $spsdfp$ cross-shell interaction for the shell model was successfully fitted to a wide range of mostly intruder negative parity states of the $sd$ shell nuclei. This paper reports the application of the FSU interaction to systematically trace out the relative positions of the effective single-particle energies of the $0f_{7/2}$ and $1p_{3/2}$ orbitals, the evolution from normally ordered low-lying states to the "Island of Inversion" (IoI), and the behavior of a wide range of excited states with a $0f_{7/2}$ proton and neutron coupled to maximum spin of $7 \hbar$. Above a proton number of about 13 the $0f_{7/2}$ orbital lies below that of $1p_{3/2}$, which is considered normal ordering, but systematically at $Z = 10$ to $12$ the orbitals cross. The calculations reproduce well the 2p2h - 0p0h inversion in the configurations of nuclei inside the IoI, they reproduce the absolute binding energies and the transition to normal ordering as the proton number approaches that of the neutrons. The important role of $1p_{3/2}$ neutron pairs in the IoI is also demonstrated. The calculations account well for the energies of the fully aligned states with 0, 1, or 2 individual $sd$ nucleon aligned in spin with the aligned $\pi 0f_{7/2}$ - $\nu 0f_{7/2}$ pair and reproduce well their systematic variation with $A$ and number of aligned $sd$ nucleons. The results presented in this paper give hope for the predictive power of the FSU interaction for more exotic nuclei to be explored in near future

Reorientation-effect measurement of the first 2+ state in 12C : Confirmation of oblate deformation

A Coulomb-excitation reorientation-effect measurement using the TIGRESS γ−ray spectrometer at the TRIUMF/ISAC II facility has permitted the determination of the 〈21 +‖E2ˆ‖21 +〉 diagonal matrix element in 12C from particle−γ coincidence data and state-of-the-art no-core shell model calculations of the nuclear polarizability. The nuclear polarizability for the ground and first-excited (21 +) states in 12C have been calculated using chiral NN N4LO500 and NN+3NF350 interactions, which show convergence and agreement with photo-absorption cross-section data. Predictions show a change in the nuclear polarizability with a substantial increase between the ground state and first excited 21 + state at 4.439 MeV. The polarizability of the 21 + state is introduced into the current and previous Coulomb-excitation reorientation-effect analyses of 12C. Spectroscopic quadrupole moments of QS(21 +)=+0.053(44) eb and QS(21 +)=+0.08(3) eb are determined, respectively, yielding a weighted average of QS(21 +)=+0.071(25) eb, in agreement with recent ab initio calculations. The present measurement confirms that the 21 + state of 12C is oblate and emphasizes the important role played by the nuclear polarizability in Coulomb-excitation studies of light nuclei