Scissors Modes
{{short description|Collective excitations}}
{{Orphan|date=February 2025}}
Scissors Modes are collective excitations in which two particle systems move with respect to each other conserving their shape.
For the first time they were predicted to occur in deformed atomic nuclei by N. LoIudice and F. Palumbo,{{cite journal | last1 = Iudice | first1 = N. Lo | last2 = Palumbo | first2 = F. | year = 1978| title = New Isovector Collective Modes in Deformed Nuclei| journal = Physical Review Letters| publisher=American Physical Society (APS) | volume = 41 | issue = 22 | pages = 1532–1534 | doi = 10.1103/PhysRevLett.41.1532 | bibcode=1978PhRvL..41.1532I| issn=0031-9007}} who used a semiclassical Two Rotor Model, whose solution required a realization of the O(4) algebra that was not known in mathematics. In this model protons and neutrons were assumed to form two interacting rotors to be identified with the blades of scissors. Their relative motion (Fig.1) generates a magnetic dipole moment whose coupling with the electromagnetic field provides the signature of the mode.
File:Scissors-20130122-wiki.pdf
Such states have been experimentally observed for the first time by A. Richter and collaborators{{cite journal | last1 = Bohle | first1 = D. | last2 = Richter | first2 = A. | last3 = Steffen | first3 = W. | last4 = Dieperink | first4 = A. E. L. | last5 = Iudice | first5 = N. Lo | last6 = Palumbo | first6 = F. | last7 = Scholten | first7 = O. | year = 1984 | title = New magnetic dipole excitation mode studied in the heavy deformed nucleus 156Gd by inelastic electron scattering| doi = 10.1016/0370-2693(84)91099-2 | journal = Physics Letters B| publisher=Elsevier BV | volume = 137 | issue = 1–2| pages = 27–31 | bibcode = 1984PhLB..137...27B| issn=0370-2693 | url = https://www.rug.nl/research/portal/en/publications/new-magnetic-dipole-excitation-mode-studied-in-the-heavy-deformed-nucleus-gd156-by-inelastic-electronscattering(bd9c55b2-eebb-4ece-a096-577997e50e15).html | hdl = 11370/bd9c55b2-eebb-4ece-a096-577997e50e15 | s2cid = 120408708 | hdl-access = free }} in a rare earth nucleus, 156Gd, and then systematically investigated experimentally and theoretically in all deformed atomic nuclei.
Inspired by this, D. Guéry-Odelin and S. Stringari{{cite journal | last1 = Guéry-Odelin | first1 = D. | last2 = Stringari | first2 = S. | year = 1999| title = Scissors Mode and Superfluidity of a Trapped Bose-Einstein Condensed Gas| journal = Physical Review Letters| publisher=American Physical Society (APS) | volume = 83 | issue = 22| pages = 4452–4455 | doi = 10.1103/PhysRevLett.83.4452 | bibcode=1999PhRvL..83.4452G| arxiv = cond-mat/9907293| s2cid = 119465641 | issn=0031-9007}} predicted similar collective excitations in Bose-Einstein condensates in magnetic traps. In this case one of the blades of the scissors must be identified
with the moving cloud of atoms and the other one with the trap. Also this excitation mode was experimentally confirmed.{{cite journal | last1 = Maragò | first1 = O. M. | last2 = Hopkins | first2 = S. A. | last3 = Arlt | first3 = J. | last4 = Hodby | first4 = E. | last5 = Hechenblaikner | first5 = G. | last6 = Foot | first6 = C. J. | year = 2000| title = Observation of the Scissors Mode and Evidence for Superfluidity of a Trapped Bose-Einstein Condensed Gas| journal = Physical Review Letters| publisher=American Physical Society (APS) | volume = 84 | issue = 10 | pages = 2056–2059 | doi = 10.1103/PhysRevLett.84.2056 | bibcode=2000PhRvL..84.2056M | pmid=11017208| arxiv = cond-mat/9911195| s2cid = 22897316 | issn=0031-9007 }}
In close analogy similar collective excitations have predicted in a number of other systems, including metal clusters,{{cite journal | last1=Lipparini | first1=E. | last2=Stringari | first2=S. | title=Rotational magnetic state in deformed metal clusters | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=63 | issue=5 | date=31 July 1989 | issn=0031-9007 | doi=10.1103/physrevlett.63.570 | pmid=10041109 | pages=570–572| bibcode=1989PhRvL..63..570L }} quantum dots,{{cite journal | last1=Serra | first1=Llorenç | last2=Puente | first2=Antonio | last3=Lipparini | first3=Enrico | title=Orbital current mode in elliptical quantum dots | journal=Physical Review B | publisher=American Physical Society (APS) | volume=60 | issue=20 | date=15 November 1999 | issn=0163-1829 | doi=10.1103/physrevb.60.r13966 | pages=R13966–R13969|arxiv=cond-mat/9909135| bibcode=1999PhRvB..6013966S | s2cid=15101298 }} Fermi condensates{{cite journal | last1=Minguzzi | first1=Anna|author1-link=Anna Minguzzi | last2=Tosi | first2=Mario P. | title=Scissors mode in a superfluid Fermi gas | journal=Physical Review A | volume=63 | issue=2 | date=16 January 2001 | issn=1050-2947 | doi=10.1103/physreva.63.023609 | page=023609|arxiv=cond-mat/0005098| bibcode=2001PhRvA..63b3609M| s2cid=119079410 }} and crystals,{{cite journal | last1=Hatada | first1=Keisuke | last2=Hayakawa | first2=Kuniko | last3=Palumbo | first3=Fabrizio | title=Scissors mode and dichroism in an anisotropic crystal | journal=Physical Review B | publisher=American Physical Society (APS) | volume=71 | issue=9 | date=21 March 2005 | issn=1098-0121 | doi=10.1103/physrevb.71.092402 | page=092402|arxiv=cond-mat/0402193| bibcode=2005PhRvB..71i2402H | s2cid=119331352 }} but none of them has yet been experimentally investigated or found.