We prove a general quadratic formula for basic hypergeometric series, from which simple proofs of several recent determinant and Pfaffian formulas are obtained. A special case of the quadratic formula is actually related to a Gram determinant formula
for Askey-Wilson polynomials. We also show how to derive a recent double-sum formula for the moments of Askey-Wilson polynomials from Newtons interpolation formula.
The longitudinal momentum distribution (P_{//}) of fragments after one-proton removal from ^{23} Al and reaction cross sections (sigma_R) for ^{23,24} Al on carbon target at 74A MeV have been measured. The ^{23,24} Al ions were produced through pro
jectile fragmentation of 135 A MeV ^{28} Si primary beam using RIPS fragment separator at RIKEN. P_{//} is measured by a direct time-of-flight (TOF) technique, while sigma_R is determined using a transmission method. An enhancement in sigma_R is observed for ^{23} Al compared with ^{24} Al. The P_{//} for ^{22} Mg fragments from ^{23} Al breakup has been obtained for the first time. FWHM of the distributions has been determined to be 232 pm 28 MeV/c. The experimental data are discussed by using Few-Body Glauber model. Analysis of P_{//} demonstrates a dominant d-wave configuration for the valence proton in ground state of ^{23} Al, indicating that ^{23} Al is not a proton halo nucleus.
