In further comments, John Van Vleck pays particular attention to (1) the 1925 study of the spectra of hydrogen and ionized helium, that J.V.V. considers one sentence short of proposing electron spin (which would have led to sharing a Nobel prize), and (2) what J.V.V. regards as Slater's greatest paper, that introduced the mathematical object now called the Slater determinant. "These were some of the achievements (that led to his) election to the National Academy ... at ... thirty-one. He played a key role in lifting American theoretical physics to high international standing." Slater's doctoral students, during this time, included Nathan Rosen Ph.D. in 1932 for a theoretical study of the hydrogen molecule, and William Shockley Ph.D. 1936 for an energy band structure of sodium chloride, who later received a Nobel Prize for the discovery of the transistor.