@article{c54f256d49ee4d5294b71d6ed92916c5,

title = "Two-particle ladder diagrams and double-counting in effective interaction calculations",

abstract = "It is shown that including the two-particle ladder diagrams, computed with the Barrett, Hewitt, McCarthy G matrix elements at a starting energy of 47 MeV and for intermediate excitations of 2ℏΩ, in the perturbation expansion for the effective two-body interaction in mass-18 nuclei involves a double-counting of roughly 42%. It is argued by comparison that the double-counting should be roughly the same when the Kuo G matrix elements are used.",

author = "Barrett, {B. R.} and Kirson, {M. W.}",

note = "Funding Information: A recurring problem \[1\]i n calculations of the effective interaction q~ is the question of how much double-counting is caused when the two-particle ladder diagram, shown in fig. 1, called G2p and computed with plane.wave intermediate-state G matrix elements and ~termediate excitations of 2hi2, is included in the perturbation expansion for q~ .The problem has been most widely studied and discussed for calculations for mass-18 nuclei \[2\]u sing the Kuo G matrix elements \[3\]c omputed from the Hamada-Johnston hard-core potential \[4\]K. uo found that including G2p in q~ helped to improve the agreement of the calculated spectra with the experimental spectra for mass-18 nuclei. Including G2p obviously involves double-counting, since the nuclear reaction matrix G is the sum of all two-particle ladder diagrams in the free nucleon potential V, as shown diagrammatically and algebraically in fig. 2. Kuo commented on this double-counting and suggested that it would be small, since his G matrix elements were computed with plane-wave intermediate states, which favor the contributions to G coming from intermediate states of high-excitation energies, thereby leaving out most of the contribution from low-excitation energies. Calculations by Brown and Wong \[5\]a lso estimated this double-counting to be small (however these calculations contain an error * Work supported in part by the NSF, Grant GP-39030X1. * Alfred P. Sloan Foundation Research Fellow, 1972-74.",

year = "1975",

month = feb,

day = "3",

doi = "10.1016/0370-2693(75)90423-2",

language = "English (US)",

volume = "55",

pages = "129--133",

journal = "Physics Letters B",

issn = "0370-2693",

publisher = "Elsevier",

number = "2",

}