From owner-chemistry@ccl.net Wed Dec 23 12:15:00 2020 From: "Dr.N Sukumar n.sukumar::snu.edu.in" To: CCL Subject: CCL: why is there no 2d subshell in atoms Message-Id: <-54248-201223024215-5878-abj6zFEF+vxut26RVtuBog,server.ccl.net> X-Original-From: "Dr.N Sukumar" Content-Type: multipart/alternative; boundary="000000000000f966fb05b71cd33f" Date: Wed, 23 Dec 2020 13:11:55 +0530 MIME-Version: 1.0 Sent to CCL by: "Dr.N Sukumar" [n.sukumar ~ snu.edu.in] --000000000000f966fb05b71cd33f Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable It has to do with the nature of the potential. Atomic orbitals are solutions of the Hamiltnian in a spherically symmetric potential; the radial part of the solutions are the spherical harmonics Ylm. In a disk jellium model, for instance (often used in 2d clusters), you do find 1f and 2d orbitals. *N. SukumarProfessor of ChemistryDirector, Center for Informatics**Shiv Nadar University, India* https://chemistry.snu.edu.in/people/faculty/n-sukumar "The belief that there is only one truth is the deepest root of evil in the world." =E2=80=94 Max Born On Wed, Dec 23, 2020 at 11:14 AM Thomas Manz thomasamanz++gmail.com < owner-chemistry,,ccl.net> wrote: > Dear colleagues, > > I am looking for a reference to cite that provides mathematical details a= s > to why a 2d subshell does not exist for an atom. I understand the > traditional pat answer that n >=3D L+1 where L is angular quantum number = ( L > =3D 0 for s, 1 for p, 2 for d, etc.) and n is the principal quantum numbe= r. I > would like to understand the mathematical and physical reason for this, > preferably with some kind of mathematical derivation. Does anyone know a > good reference for this? > > Although the above question seems "simple", I believe there more to it > than first meets the eye. Specifically, such a rule does not apply to the > nucleons inside an atomic nucleus. In nuclear models (e.g., nuclear shell > model), for example, they encounter things such as the 1f orbitals. Why > does such an orbital exist for nucleons but not for electrons, when both > are spin 1/2 fermions? The physical interaction (coupling regime) must ha= ve > something to do with whether or not the 1f orbital exists for a particula= r > fermion. In the case of nucleons, there is a very strong pairing so that > two nucleons practically pair to make an effective boson; however, it is = my > understanding that for nucleons with odd-numbered nucleons, the odd nucle= on > can still exist in orbitals such as 1f. The spin-orbit coupling is > substantial for nucleons, but also substantial for electrons in heavy > elements. > > I would appreciate any mathematical or physical insights as well > references to understand what is going on here. > > Sincerest thanks, > > Tom Manz > --000000000000f966fb05b71cd33f Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
It has to do with the nature of the potential. Atomic orbi= tals are solutions of the Hamiltnian in a spherically symmetric potential; = the radial part of the solutions are the spherical harmonics Ylm. In a disk= jellium model, for instance (often used in 2d clusters), you do find 1f an= d 2d orbitals.
=
N. S= ukumar
Professor of Chemistry
Director, Center for Informatics
Shiv Nadar University, India
https://chemistry.snu.edu.in/people/faculty/n-suk= umar

"The belief that there is only one truth is = the deepest root of evil in the world."

=E2=80=94 Max = Born


=
On Wed, De= c 23, 2020 at 11:14 AM Thomas Manz thomasamanz++gmail.com <owner-chemis= try,,ccl.net> wrote:
Dear colleagues,

I am lookin= g for a reference to cite that=C2=A0provides mathematical details as to why= a 2d subshell does not exist for an atom. I understand the traditional=C2= =A0pat answer that n >=3D L+1 where L is angular quantum number ( L =3D = 0 for s, 1 for p, 2 for d, etc.) and n is the principal quantum number. I w= ould like to understand the mathematical and physical reason for this, pref= erably with some kind of mathematical derivation. Does anyone know a good r= eference for this?

Although the above question see= ms "simple", I believe=C2=A0there more to it than first meets the= eye. Specifically, such a rule does not apply to the nucleons inside an at= omic nucleus. In nuclear=C2=A0models (e.g., nuclear shell model), for examp= le, they encounter things such as the 1f orbitals. Why does such an orbital= exist for nucleons but not for electrons, when both are spin 1/2 fermions?= The physical interaction (coupling regime) must have something to do with = whether or not the 1f orbital exists for a particular fermion. In the case = of nucleons, there is a very strong pairing so that two nucleons practicall= y pair to make an effective boson; however, it is my understanding that for= nucleons with odd-numbered nucleons, the odd nucleon can still exist in or= bitals such as 1f. The spin-orbit coupling is substantial for nucleons, but= also substantial for electrons in heavy elements.

I would appreciate any mathematical or physical insights as well reference= s to understand what is going on here.

Sincerest t= hanks,

Tom Manz
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