Ytterbium-167

Abstract

Proton bombardment of pure Tm 2 0 3 , followed by ion-exchange separations, has yielded an activity with an 18.5-minute half-life. Determination of the excitation function and identification of the daughter Tm 167 assigns the activity to Yb 167 . A gamma-ray spectrum shows it to decay by electron capture with a 0.118 Mev and possibly other gamma rays.

Novel vacuum conditions in inflationary collapse models

“…(10), is identical to Eq. (15), which is the one obtained by the authors of [41] when m = 0. In particular, it involves the quantity a ′′ a .…”

“…In order to avoid the issues raised against Hamiltonian diagonalization, the authors in [41] motivated different initial conditions from the minimization of the renormalized stress-energy density. The authors in [41], start from the action for a scalar field φ with mass m,…”

“…(15), but replacing a ′′ a → z ′′ z , where z ≡ √ 2ǫ 1 aM P . In other words, the quantum theory proposed by the authors of [41] is better suited for the field y k (η), than for the Mukhanov-Sasaki variable because strictly if ǫ ′ 1 = 0, then a ′′ a = z ′′ z . Therefore, we consider once again, the general solution (11), which is…”

“…Another related issue is that usual renormalization methods, which make 0|Ĥ(η i )|0 finite, can only be defined at η i → −∞, that is, at the very early stages of inflation. Some authors consider those arguments sufficient to find alternatives to the Hamiltonian diagonalization method [39][40][41]. Here it is also important to mention that different choices other than the BD vacuum state have been analyzed previously.…”

“…One of the possible alternatives is proposed in Ref. [41]. Those authors suggest that, instead of minimizing 0|Ĥ|0 , one should focus on minimizing the renormalized T 00 (x) .…”