We report on robust measurements of elemental abundances of the Type IIn supernova SN 1978K, based on the high-resolution X-ray spectrum obtained with the Reflection Grating Spectrometer (RGS) onboard XMM-Newton. The RGS clearly resolves a number of
emission lines, including N Ly$alpha$, O Ly$alpha$, O Ly$beta$, Fe XVII, Fe XVIII, Ne He$alpha$ and Ne Ly$alpha$ for the first time from SN 1978K. The X-ray spectrum can be represented by an absorbed, two-temperature thermal emission model, with temperatures of $kT sim 0.6$ keV and $2.7$ keV. The elemental abundances are obtained to be N $=$ $2.36_{-0.80}^{+0.88}$, O $=$ $0.20 pm{0.05}$, Ne $=$ $0.47 pm{0.12}$, Fe $=$ $0.15_{-0.02}^{+0.01}$ times the solar values. The low metal abundances except for N show that the X-ray emitting plasma originates from the circumstellar medium blown by the progenitor star. The abundances of N and O are far from CNO-equilibrium abundances expected for the surface composition of a luminous blue variable, and resemble the H-rich envelope of less-massive stars with masses of 10-25 M$_odot$. Together with other peculiar properties of SN 1978K, i.e., a low expansion velocity of 500-1000 km s$^{-1}$ and SN IIn-like optical spectra, we propose that SN 1978K is a result of either an electron-capture SN from a super asymptotic giant branch star, or a weak Fe core-collapse explosion of a relatively low-mass ($sim$10 M$_odot$) or high-mass ($sim$20-25 M$_odot$) red supergiant star. However, these scenarios can not naturally explain the high mass-loss rate of the order of $dot{M} sim 10^{-3} rm{M_{odot} yr^{-1}}$ over $gtrsim$1000 yr before the explosion, which is inferred by this work as well as many other earlier studies. Further theoretical studies are required to explain the high mass-loss rates at the final evolutionary stages of massive stars.
The cluster states in $^{13}{rm C}$ are investigated by antisymmetrized molecular dynamics. By investigating the spectroscopic factors, the cluster configurations of the excited states are discussed. It is found that the $1/2^+_2$ state is dominantly
composed of the $^{12}{rm C}(0^+_2)otimes s_{1/2}$ configuration and can be regarded as a Hoyle analogue state. On the other hand, the p-wave states ($3/2^-$ and $1/2^-$) do not have such structure, because of the coupling with other configurations. The isoscalar monopole and dipole transition strengths from the ground to the excited states are also studied. It is shown that the excited $1/2^-$ states have strong isoscalar monopole transition strengths consistent with the observation. On the other hand, the excited $1/2^+$ states unexpectedly have weak isoscalar dipole transitions except for the $1/2^+_1$ state. It is discussed that the suppression of the dipole transition is attributed to the property of the dipole operator.
The alpha cluster states of 16C are investigated by using the antisymmetrized molecular dynamics. It is shown that two different types of alpha cluster states exist: triangular and linear-chain states. The former has an approximate isosceles triangul
ar configuration of alpha particles surrounded by four valence neutrons occupying sd-shell, while the latter has the linearly aligned alpha particles with two sd-shell neutrons and two pf-shell neutrons. It is found that the structure of the linear-chain state is qualitatively understood in terms of the 3/2 pi- and 1/2 sigma- molecular orbit as predicted by molecular-orbital model, but there exists non-negligible Be+alpha+2n correlation. The band-head energies of the triangular and linear-chain rotational bands are 8.0 and 15.5 MeV, and the latter is close to the He+Be threshold energy. It is also shown that the linear-chain state becomes the yrast sstate at J=10 with excitation energy 27.8 MeV owing to its very large moment-of-inertia comparable with hyperdeformation.
