At present, available information on r;-N interactions can be obtained only*) from the process 7r-+p~r;+n. In this note we determine the coupling constant gNNn using the dispersion relation of the amplitudes for the r;-production_The dispersion relation includes an integral over a wide range of energy from the low energy region below the r;~N threshold to the high energy region_ **) In order to avoid the unknown parts involved in this integral, we consider the dispersion relation for partial wave amplitudes_ Among various partial waves, we exclusively consider a particular one for which the contribution from the integral becomes negligibly small as compared with that from the Born term.The P13 wave is appropriate for this purpose in the reaction 7r -+ p~r;+ n according to the results of a preceding paper_I)The. following dispersion relation for the PI3 wave is obtained in the same way as in the paper of C.G_L.R2) which is valid near the r;N threshold:[~ll=If1,,,:n+~ 1 v(E1 +M)(E2 +M)

Higher-order composite fermion states are correlated with many quasiparticles. The energy calculations are very complicated. We develop the theory of Tao and Thouless to explain them. The total Hamiltonian is (H D + H I), where H D includes Landau energies and classical Coulomb energies. We find the most uniform electron configuration in Landau states which has the minimum energy of H D. At ν = (2 j − 1)/(2 j), all the nearest electron pairs are forbidden to transfer to any empty states because of momentum conservation. Therefore, perturbation energies of the nearest electron pairs are zero in all order of perturbation. At ν = j/(2 j − 1), j/(2 j + 1), all the nearest electron (or hole) pairs can transfer to all hole (or electron) states. At ν = 4/11, 4/13, 5/13, 5/17, 6/17, only the specific nearest hole pairs can transfer to all electron states. For example, the nearest-hole-pair energy at ν = 4/11 is lower than the limiting energies from both sides (the left side ν = (4s + 1)/(11s + 3) and the right side ν = (4s − 1)/(11s − 3) for infinitely large s). Thus, the nearest-hole-pair energy at specific ν is different from the limiting values from both sides. The property yields energy gap for the specific ν. Also gapless structure appears at other filling factors (e.g., at ν = 1/2).

Energy dependent partial wave anlyses for the reaction rc-+p ':"'J+n are carried out with respect to S, P, D and F waves in the energy range 561-1300 MeV. Two different types of the solutions are obtained. In the first solution, the "'J-production peak is dominated by the S 11 resonance with mass M = 1570 MeV, total width TT = 140 MeV, branching ratios (S 11 res. --->rcN) I (S 11 res.->all) =40% and (S 11 res.-----'7"1JN)/(S 11 res.--'lall) =50%. In the second solution, it is dominated by the P 11 resonance with M=1580 MeV, TT=130 MeV, (P 11 res.-'TrcN)/(P 11 res.-----'7all) =35% and (P 11 res.-?"'JN)j(P 11 res.-'Tall) =305-~-This P 11 resonance is a new one which is different from Roper's resonance. In this analysis the second solution_ is better fitting experimental data than the first solution.P 11 and D 13 • When the peak is dominated by a resonance (called the Resonant Case) , we can consider the following three cases ;

No abstract

Under the assumption that isospin T is a good quantum number, isobaric analog states and various analogous transitions are expected in isobars with mass number A. The strengths of T z = ±3/2→ ±1/2 analogous Gamow-Teller (GT) transitions and analogous M1 transitions within the A = 41 isobar quartet are compared in detail. The T z = +3/2→ +1/2 GT transitions from the J =3/2 + ground state of 41 K leading to excited J =1/2 + , 3/2 + , and 5 / 2 + states in 41 Ca were measured using the ͑ 3 He, t͒ charge-exchange reaction. With a high energy resolution of 35 keV, many fragmented states were observed, and the GT strength distribution was determined up to 10 MeV excitation energy ͑E x ͒. The main part of the strength was concentrated in the E x =4-6 MeV region. A shell-model calculation could reproduce the concentration, but not so well details of the strength distribution. The obtained distribution was further compared with two results of 41 Ti ␤ decay studying the analogous T z =−3/2→ −1 / 2 GT strengths. They reported contradicting distributions. One-to-one correspondences of analogous transitions and analog states were assigned up to E x = 6 MeV in the comparison with one of these 41 Ti ␤-decay results. Combining the spectroscopic information of the analog states in 41 Ca and 41 Sc, the most probable J values were deduced for each pair of analog states. It was found that 5 / 2 + states carry the main part of the observed GT strength, while much less GT strength was carried by 1 / 2 + and 3 / 2 + states. The gross features of the GT strength distributions for each J were similar for the isospin analogous T z = ±3/2→ ±1/2 transitions, but the details were somewhat different. From the difference of the distributions, isospin-asymmetry matrix elements of Ϸ8 keV were deduced. The Coulomb displacement energy, which is sensitive to the configuration of states, showed a sudden increase of about 50 keV at the excitation energy of 3.8 MeV. The strengths of several M1 transitions to the IAS in 41 Ca were compared with the strengths of analogous GT transitions. It was found that ratios of the M1 and GT transition strengths were similar, suggesting that the contributions of the ᐉ term in M1 transitions are small.