Роль пионов в адронных моделях

С.И. Сухоручкин

ФГБУ Петербургский Институт Ядерной Физики 188300 Гатчина

…NEEDS IN INSTRUMENTATION FOR NUCLEAR PHYSICS by S. Devons, Manchester, 1961

• “… it is a natural temptation to make comparisons between the present stage in the study of nuclear structure with the exploration of atomic structure in Rutherford’s time … Rutherford used the bold, direct approach, what one might designate as the “high-energy” approach…”

• “The more subtle “low-energy” investigations, for example the study of optical spectra, only became a fruitful means of examining the refined details of atomic structure after Rutherford’s direct approach led to the Bohr theory, and the subsequent development of quantum mechanics. … distinction between high and low energy phenomena is perhaps not so clear as in atomic structure.

• The existence of highly developed … quantum-mechanics, makes it possible to drow inferences about basic underlying features from observation and sophisticated interpretation of refined detailes.”

• • “… since the nucleons of which the nucleus is composed are far from simple

entities, one may suspect (or hope?) that there are still to be discovered subtle features of complex nuclei which reflect underlying properties of nucleons, and which may even prove difficult to observe in direct study of the elementary particles themselves.” ---------------------------------------------

• “More directly in such cases as the study of some elementary-particles or high-energy process can be facilitated by observation of phenomena involving complex nuclei, the fullest possible understanding of nuclear structure becomes a pre-requisite.”

COMPILATIONS OF NUCLEAR DATA USED IN PRESENT DATA ANALYSIS

(1), RESULTS

• 1) LANDOLDT-BOERNSTEIN COMPLEX CATALOG, 2000 by W. Martienssen:• “The importance of collection of selected and easily retrievable data was recognized long ago

and now such activity appears even more important than ever due to the immense production rate of literature and data as well as due to the steady growing interdependence between increasingly differentiated research fields.”

• 16 vols of Landoldt-Boernstein Compilation, Ed. H.Schopper, Authors S.I.Sukhoruchkin, Z.N.Soroko

• LB vol. I/16B 1998, LB vol. I/16C 2000, LB vol.1/24 2010 Neutron Resonance Parameters • LB vol. I/19A1 1999, vol.I/19A2 2000 Nuclear States from Charge Particle Reactions, • LB vol. I/22AB 2000 Nuclear Binding Energies and Atomic Masses,• LB vol. I/19B1 2000, vol.I/19B2 2000, vol.I/19B3 2000, vol.I/19C 2008, • LB vol.I/25a-e, 2012, 5 volumes., Excited Nuclear States Z<29,Z=30-47,Z=48-60,Z=61-73, 74-

102• 2) Results: Cluster effects in nuclear binding energies, Bruss. 2010, S.Sukhoruckin,

D.Sukhoruchkin • Hadron-2011, The role of pion-exchange tensoe forces in nuclear excitations, S.Sukhoruchkin• ISINN-19, Compilation of nuclear excited state CRF, S.Sukhoruchkin, Z..Soroko,

D.Sukhoruchkin • ISINN-19, Compilation of nuclear binding energies MDF, S.Sukhoruchkin, D.Sukhoruchkin

(2011)• ISINN-19, Study of nonstatistical effects due to tensor forces, S.Sukhoruchkin, M.Sukhoruchkina• ISINN-17, The origin of tuning effects in nuclear data, JINR publ. E3-2010-36, S.Sukhoruchkin

Fig. 2. Intuitive illustration of tensor forces acting between two nucleons on orbits j and j'.

Observed earlier Groping Effect in Energies of Excited States of all nuclei withA<70andA<150at E*=2me and Do close to particle mass differences was named

“tuning effect” in nuclear data.Top left: Sum excitatrion distribution in Z-odd nuclei Z=19-29. Top right: D-distribution in Co-56.

Bottom: D-distributions in intervals of 0-600 and 900-1000 keV in F-18.

Table 1. Top: Comparison of E* in near-magic nuclei with multiple values of spin-flip effect in 10B (εo =1022 keV=2me); Bottom: Excitations in near-

magic 101,103Sn, 123-133Sb close to εo /6=me/3,dmN/8

• AZ 10B 10B 12C 18Ne 55Co (Fig.2)• 0+,1+ 2- 0+1 0+(T=2) 0+1 0+2 Dij Dij• E*, Dij, keV 1021.8(2) 5110.3 7654.2 27595(2) 3576.2 4590(8) 512 682• n(εo) 1 5 15/2 27 7/2 9/2 1/2 3/4• nx εo 1022 5110 7665 27594 3577 4599 511 683• Diff. 0.2(2) 0.3 1(2) 9(8)• --------------------------------------------------------------------------------------------------------------------------• 101Sn 103Sn 123Sb 125Sb 125Sb 127Sb 129Sb 131Sb 133Sb• 171.7(6) 168.0(1) 160.3(1) 332.1 643.2 491.2 645.2(1) 798.5 962.3(1)• me/3 me/3 (1/8) δmN (2/8) δmN (4/8) δmN (3/8) δmN (4/8) δmN (5/8) δmN (6/8)δmN

170.3 170.3 161.7 323.3 646.7 485.0 646.7 808.3 970.0

D-distribution in 122,124Sb

Distribution of intervals adjacent to D=x=478.5 keV in 90Y

resonances; D-distribution in 38Ar

Isotope distributions for Z=6-100

• This “tuning effect” was confirmed by maxima at 160 keV and 962 keV=6x160 keV in spacing distributions of levels in 122,124Sb (Fig. 1, left) and 133Sb as well as by stable intervals rational to the parameter 6x170 keV=εo=1022 keV found in light nuclei -- near-magic 10B, 12C, 55Co (Table 1, top)..

• New analysis of tuning effects in excitations of all nuclei (situated at different parts of nuclear shells) was performed in this work using compilation of nuclear excitations Springer, LB vol. I/25.

• Numbers of isotopes (for each Z) in which stable intervals D close to D=nx160 keV + mx 170 keV (n,m integers 0,1…12) were observed are presented in Fig.3 as a histogram for different Z.

• Combined D=492 keV=2x160 keV+170 keV, D=672 keV=160keV+3x170 keV are included. Arrows in top part of Figure 3 correspond to closed shells, arrows at bottom show additional maxima in nuclei where a large proton shell 1i9/2 is filled (Z=68,72,76,78).

• Observed in Sb isotopes systematic linear trend corresponds to the same large 1g9/2 neutrom shell (with Z=51, valence proton in 1g7/2 shell). In both cases neutron and proton are moving in shells with different spin-orbit orientation.

Isotope distributions for Z=6-100

Spacing distribution of levels in 89Y (number of states n=388, ΔE=3 and 5 keV).

D-distribution of levels in 90Y (n=190) at low-energy and in

neutron resonances (n=692).

Distribution of intervals adjacent to D=x=478.5 keV in 90Y

resonances; D-distribution in 38Ar

Sp for Z=51

• Simultaneously with the above described analysis of tunung effects in nuclear excitations the same

• parameters eo were found in differences of nuclear binding energies. Integer values of this parameter were observed in two- and four-proton separation energies and cluster effects in many nuclei (Fig.4).

• In Sb-isotopes the linear trend in Sp is due to constancy of interaction parameter ep2n=680 keV=2/3 εo.

Sp for Z=51

S2p for Z=78, 84

• The largest maximum in number of parameter distribution (Fig.3) corresponds to platinum isotopes (Z=78). A linear dependence of two-proton separation energies (for Z=78,84) as a function of N is shown in Fig 5. The slope of a trend is 340 keV= εo/3, similar to that in Z=84 isotopes seen at right.

Sum distributions of excitations in nuclei with Z=79 and Z-84,

ΔE=7 keV).

S2p for Z=78, 84

• The largest maximum in number of parameter distribution (Fig.3) corresponds to platinum isotopes (Z=78). A linear dependence of two-proton separation energies (for Z=78,84) as a function of N is shown in Fig 5. The slope of a trend is 340 keV= εo/3, similar to that in Z=84 isotopes seen at right.

Observed tuning effect in nuclear data is considered in view of

Nambu suggestion for a search for relations in particle masses • 1) Nambu himself pointed out relations with pion mass in particle spectrum :

mLambda=8mpi (1952) • 2) Samios at al (Particle Data Group) found coincidence of mOmega-mksi =137

MeV with mpi• 3) R.Sternheimer noticed coincidence of meta’-meta=meta-mpi=409 MeV with

mp+2mpo• 4) Wick and Sternheimer noticed stable mass intervals Mq’’=momega/2 and

Mq=mN-mK=441 MeV• 5) P. Kropotkin noticed that Sternheimer’s parameter Mq is close to

me/3=1324/3=441 MeV • 6) mu/Z =115.9x10-5 alpha/2p=115.9x10-5• 7) me/3(DMD=147 MEV)=115.9x10-5• 8) Frank Wilczek notices an important role of the top-quark mass• 9) Long-range correlations with εo=2me are observed in cluster effects.• 10) Pion mass splitting close to 9me and the doubled pion beta-decay energy close

to 16me are observed as multiple parameters in nuclear cluster effects and masses of particles: pion itself, muon, nucleon delta-excitation and neutron mass itself.

Tests of the Empirical Mass Rormula m=Nx3me for Leptons and Hadrons, by R.Frosch (in 1967- 1991) Nuovo Cimento v.104A, no 6, p.913,1991

• The experimental set of 47 masses was replaced by set of 47 random numbers… the probability for random masses to fit the 3me formula better than the experimental masses is only 2x10-4.

Table 3a. Comparison of particle masses (PDG 2008) with periods 3me and 16me = δ = 8175.9825(2) (N - number of the period δ, me=510.998910(13) keV

Part. mi, MeV mi/3me N·16me N mi-N·16me Comments

µ 105.658367(4) 68.92* 106.2878 13 -0.6294 -.0511-0.118

πo 134.9766(6) 88,05* 138.9917 17 -4,0174

π± 139.5702(4) 91.04* 17 +0.5762 +0.511+0.065

ηo 547.853(24) 357.38** 547.7908 67 0.06(2)

ω 782.65(12) 510.54** 784.8943 96 -2.24(12)

φ 1019.46(2) 665.01** 1021.998 125 -2.54(2)

Κ± 493.677(16) 322.03** 490.5590 60 +3.118(16)

p 938.2720(1) 612.05* 940.2380(1) 115 -1.9660 -me-9/8δmN

n 939.5654(1) 612.89* 115 -0.6726(1) -me-1/8δmN

Σo 1192.64(2) 777.98 1193.693 146 -1.05(2) -0.51·2=-1.02

Ξo 1314.86(20) 857.71 1316.333 161 -1.47(20) -0.51·3=-1.53

Table 2a. Presentation of parameters of tuning effects in particle masses (three upper parts with x = -1,0,1) and in nuclear data (separately in binding energies x=0 and excitations x = 1,2) by the expression

(n·16me(α/2π)x)·m with QED parameter α =137-1. Values related to (2/3)mt=MH with QED parameter αZ=129-1 (mπ-me, me/3) and the shift in neutron mass nδ-mn-me are boxed.

x m n=1 n=13 n=16 n=17 n=18

-1 3/2 mt=171.2

GeV 1/2 ML3=58

1 MZ=91.2 MH=115

0 1 16me=δ mµ=105.7 (fπ=131) mπ-me mΔ-mN/2=147

MeV 3 Mq˝=mρ/2 Mq΄=420 Mq=441

Mq˝΄=mω/2 3ΔMΔ=441

0 1 2Δ-εo 106=ΔEB 130=ΔEB 140=ΔEB 147.2=ΔEB

MeV 3 441.5=ΔEB

1 1 nδ-mn-me=161.6(1) 170=me/3

keV 3, 8 δmN=1293.34(1) me=510.99891

Заключение• Эффект подстройки (tuning effect) в ядерных возбуждениях и в энергиях связи

подтверждается в данных из новых компиляций Vols. I/19, I/22, i/24, I/25 LB Springer.

• Cоотношение 3 : 2 : 1 = mt : MH : ML3 между массой тор кварка, ожидаемой массой скалярного бозона и пока неподтверждённого эффекта группирования масс в эксперименте L3 в LEP-ЦЕРН будет проверятся на новых данных ожидаемых в ближайшие годы. Структура в параметрах Стандартной Модели (массы векторных полей, скаляра) и КЭД-поправки простираются до пиона, который одновременно выступает как параметр ядерных сил и как выделенный параметр в спектре масс элементарных частиц.

• Соотношение (N·16me – me –mn)/δmN =1/8.00 в массах нуклонов и электрона и отношения в массах пионов и лептонов согласуются с предположением Намбу, что эмпирические соотношения в массах частиц могут быть важными для развития Стандартной Модели. Эффекты в ядерных данных (от пионного обмена) согласуются с предположением Девонса о возможности наблюдения фундаментальных эффектов в точных ядерных данных.

• Программы использования ядерных данных (включая данных по нейтронным резонансам) будут более обоснованными, если будет подтверждена роль КХД радиационных поправок)..

• Наблюдаемая аналогия между параметрами эффектов подстройки в массах частиц и в ядерных данных должна быть теоретически обоснована теорией (QCD-SM см. лит.).