@article{3c21540f2bb84279bd4dbabb4b8f85ca,

title = "Energies of monopole vibrations",

abstract = "The energies of the T = 0 and T = 1 monopole states in 16O are calculated to second order in perturbation theory. Terms are found which more than cancel the R.P.A. graphs; these help to push up the energy of the T = 0 state.",

author = "L. Zamick",

note = "Funding Information: The T = 0 monopole vibration (breathing mode) of 160 can be constructed by operating on the ground state with the operator ~ r2(i), summed over all particles, and keeping only that part which is orthogonal to the ground state; the T = 1 monopole state is similarly obtained using the operator ~i r2(i)'rz( i){"} If 160 is approximated by a closed shell nucleus the above states would be linear combinations of only three particle-hole states ls~ - 0s~ 1, lp~ - 0p~-1 and lp½ - 0p,~ 1. The energy of these states is 2/~o2 ~ 30 MeV, and thus the unperturbed energy of the monopole vibrations is also 2~w. But the interactions between the particles and holes may alter the mean positions of these states. It is quite important and by no means easy to obtain the mean energies. The importance lies to a great extent from the fact that these states can admix into the low lying eigenstates of the system. The T = 0 mixing may be important for determining E(0) decay rates such as the 02 -~ 01 electron positron decay from the 6.06 MeV state to ground. The T = 1 J = 0 monopole state was not considered interesting until it was pointed out by Bohr et al. \[1\] that it mixes in, more than other state, into the ground state via the isospin violating part of the Coulomb interaction. This is just a reflection of the fact that the main thing the Coulomb force does is to change the shape of the proton single particle radial wave functions relative to those of the neutron. The above states are also important in the problem of calculating the change in radius as * Permanent address: Rutgers University. Supported by Rutgers University Fellowship and Weizman In-stitute Senior Fellowship. Supported in part by the National Science Foundation. Funding Information: I would like to acknowledge conversations with M. Kirson, A. Bohr and I. Talmi and correspondence with J. Blomqvist. I thank Professor Talmi and the Weizmann Institute for their hospitality and I am grateful to Rutgers University for a travelling fellowship.",

year = "1970",

month = feb,

day = "16",

doi = "10.1016/0370-2693(70)90090-0",

language = "English (US)",

volume = "31",

pages = "160--162",

journal = "Physics Letters B",

issn = "0370-2693",

publisher = "Elsevier",

number = "4",

}