Older VMC Spectroscopic Overlaps

dp in ³He (Fig.14)

dd in ⁴He (Fig.18)

αd in ⁶Li (Fig.21)

The next files are the actual outputs of our Monte Carlo codes, containing the relevant amplitudes in momentum space and the (unsmoothed) radial overlap functions, both with their Monte Carlo statistical errors.

dp in ³He

dd in ⁴He

tp in ⁴He

αd in ⁶Li

αt in ⁷Li

αα; in ⁸Be

Here is a figure of the 4+2, 4+3, and 4+4 overlaps in different excited states: cluster.eps

The following overlaps with ⁶Li have been made with VMC wave functions as of February 2014 using the Argonne v18 + Urbana X Hamiltonian. (Urbana X is intermediate between Urbana IX and Illinois-7.)

⁵He(3/2-) 14-Feb-14

⁵Li(3/2-) 14-Feb-14

All the ⁶He and ⁶Li files below have been updated using the latest (September 2009) variational Monte Carlo (VMC) wave functions for the Argonne v18 + Urbana IX Hamiltonian.

We have calculated the overlaps of ⁷Li (3/2-) ground state with ⁶He + proton where ⁶He can be in any of five states: (0+) ground state, (2+) excited state at 1.9 MeV, (2+) excited state at 3.8 MeV, (1+) excited state at 4.3 MeV, and (0+) excited state at 5.9 MeV (theoretical excitation energies). These correspond to states that are predominantly ¹S₀, ¹D₂, ³P₂, ³P₁, and ³P₀ in character. The proton can be in p1/2, p3/2, f5/2, or f7/2 states (as permitted by angular momentum conservation). The output files with the momentum amplitudes are given below: after some header information, the amplitudes for the p1/2, p3/2, f5/2, and f7/2 are tabulated as a function of k, and then integrated spectroscopic factors are given at the end. Momentum distributions are determined by

Also included are r-space amplitudes with the normalization:

⁶He(0+) updated 18-Sep-09

⁶He(2+) updated 18-Sep-09

⁶He(2+)* updated 18-Sep-09

⁶He(1+) updated 18-Sep-09

⁶He(0+)* updated 18-Sep-09

We have also calculated the overlaps of ⁷Li (3/2-) ground state with ⁶Li + neutron where ⁶Li can be in any of five states: (1+) ground state, (3+) excited state at 3.1 MeV, (2+) excited state at 4.6 MeV, (1+) excited state at 6.0 MeV, and (1+) excited state at 11.1 MeV (theoretical excitation energies). These correspond to states that are predominantly ³S₁, ³D₃, ³D₂, ³D₁, and ¹P₁ in character. For the (0+;T=1) excited state at 3.9 MeV and the (2+;T=1) excited state at 5.9 MeV, one should use 1/2 of the corresponding ⁶He states above.

⁶Li(1+) updated 18-Sep-09

⁶Li(3+) updated 18-Sep-09

⁶Li(2+) updated 18-Sep-09

⁶Li(1+)* updated 18-Sep-09

⁶Li(1+)** updated 18-Sep-09

Here are some single-nucleon densities for these final states ⁶Li(1+,3+,0+)

New results for overlaps of ⁸Li (2+) ground state with ⁷Li + neutron where ⁷Li can be in a number of different states, starting with the (3/2-) ground state and (1/2-) first excited state at 0.48 MeV. The following files have been made with a charge-independent wave function, so they may also be used as a first approximation for ⁸B (2+) overlap with ⁷Be + proton. Output and normalization are as described above for the ⁶He files.

⁷Li(3/2-) ground state updated 10-Nov-09

⁷Li(1/2-) @ 0.48 MeV updated 10-Nov-09

⁷Li(7/2-) @ 4.65 MeV updated 09-Feb-07

⁷Li(5/2-) @ 6.60 MeV updated 09-Feb-07

⁷Li(5/2-) @ 7.45 MeV updated 10-Feb-07

⁷Li(3/2-) @ 8.75 MeV updated 10-Feb-07

⁷Li(1/2-) @ 9.09 MeV updated 10-Feb-07

⁷Li(7/2-) @ 9.57 MeV updated 11-Feb-07

Here are some single-nucleon densities for these final states ⁷Li(3/2-,1/2-)

Results for overlaps of ⁹Be (3/2-) ground state with ⁸Be(J) + neutron(j) for lowest-lying J states. Both momentum and configuration space overlaps are given, with normalizations as given above.

⁸Be(0+) updated 4/1/10

⁸Be(2+) updated 4/2/10

Results for overlaps of ⁹Be (3/2-) ground state with ⁸Li(J) + proton(j) for lowest-lying J states. Both momentum and configuration space overlaps are given, with normalizations as given above.

⁸Li(2+) updated 30-Dec-10

⁸Li(1+) updated 30-Dec-10

⁸Li(3+) updated 31-Dec-10

Results for overlap of ⁹Li(3/2-) ground state with ⁸Li(J) + neutron(j). Under charge symmetry, these would correspond to overlaps ⁹C(3/2-) with ⁸B(J) + proton(j):

⁸Li(2+) updated 16-Dec-10

⁸Li(1+) updated 17-Dec-10

⁸Li(3+) updated 18-Dec-10

⁸Li(0+;2) updated 24-Feb-14

and explicitly for ⁹C(3/2-) with ⁸B(J) + proton(j):

⁸B(0+;2) updated 25-Feb-14

Here are some single-nucleon densities for these final states ⁸Li(2+,1+,3+)

Results for overlaps of ⁹Li (3/2-) ground state with ⁸He(J) + proton(j) for lowest-lying J states. Both momentum and configuration space overlaps are given, with normalizations as given above.

⁸He(0+) updated 28-Dec-10

⁸He(2+) updated 28-Dec-10

⁸He(1+) updated 28-Dec-10

⁸He(0+)* updated 29-Dec-10

⁸He(2+)* updated 29-Dec-10

Robert B. Wiringa
Last update 9 May 2016