Electroexcitation ofBe9Levels in the 14-18-MeV Region

Abstract

The form factors for electroexcitation of the lowest T =2 levels in BBe (14.39 MeV, 2 16.97 MeV, 2 ) have been measured for momentum transfers bebveen 0.5 and 1.1 fm Results are also presented for levels of unknown TJ" at 16.63 and 17.48 MeV excitation.Radiative widths have been extracted. The form factor of the 16.63-MeV state is compared with simple-spherical and deformed shell-model form factors. The ground-state rms radius and quadrupole moment have been deduced from the elastic scattering data.

Quark model calculation ofη→l+l−to all orders in the bound-state relative momentum

“…We have evaluated the electromagnetic box diagram for the leptonic decay of a pseudoscalar quark-antiquark pair with an arbitrary distribution of relative three-momentum. Quantitative results were obtained in three different models of the bound state wave function (a nonrelativistic harmonic oscillator model [12,13], a new relativistic momentum space wave function that we derived from the MIT bag model, and in the limit of extreme nonrelativistic binding, analyzed previously by Bergström [9]). Our results demonstrate that the relative branching fraction B P ≡ B(P → l + l − )/B(P → γγ) is insensitive to the details of the quark model wave function.…”

“…(25) and Ref. [9]). The harmonic oscillator and ENR results differ by less than 5% over the entire kinematical region in m l /m η .…”

“…(10) implies that the qq annihilation amplitude is proportional to the coordinate-space wave function (or its derivatives) at the origin [10,11]. This limit has been used for example to make calculations of heavy quarkonium matrix elements [16], and was used by Bergström in a calculation of P → l + l − [9].…”

“…In the limit β/m q → 0, the wave packet becomes nonrelativistic, with E p → m q . Bergström has made a quark model calculation of R in the extreme nonrelativistic (ENR) limit, taking the quark and antiquark to be at rest in the center of mass of the meson, with 2m q ≡ m P [9]. He found:…”

“…1. This approach was considered by Bergström [9] in the limit of extreme nonrelativistic binding, where the bound state quarks are assumed to be at rest in the center of mass of the meson (and the meson mass is assumed to be exactly twice the quark rest mass). These approximations must be viewed with caution however when applied to light mesons such as the η.…”