4 papers
An Improved Nonexistence Bound for the Liquid Drop Model
Marvin R. Schulz
For Gamow's liquid drop model, we improve the nonexistence bound of Frank-Killip-Nam from 8 to 7.5. The key additional input is a geometric perimeter inequality arising from the ca…
On the Efimov Effect for Four Particles in Dimension Two
Jonathan Rau, Marvin R. Schulz
We prove that the Schrödinger operator describing four particles in two dimensions, interacting solely through short-range three-body forces, can possess infinitely many bound sta…
On the Excess Charge Problem of Atoms
Dirk Hundertmark, Nikolaos Pattakos, Marvin Raimund Schulz
This paper establishes new bounds on the maximum number of electrons that an atom with nuclear charge can bind. Specifically, we show that \begin{equation*} N_c(Z) <…
Why a System of Three Bosons on Separate Lines Can Not Exhibit the Confinement Induced Efimov Effect
Dirk Hundertmark, Marvin R. Schulz, Semjon Vugalter
We study a system of three bosons interacting with short-range potentials which can move along three different lines. Two of these lines are parallel to each other within one plane…