T-INVARIANCE AND NUCLEAR FISSION

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1 T-INVARIANCE AND NUCLEAR FISSION S.G. Kdesky Voroezh Stte Uiversity, 94006, Voroezh, Uiversitetsky pl., 1, Russi, E-il:

2 1. INTRODUCTION The i of this rticle is to deostrte tht the usig of the T-ivrice coditio for yprticles ultistep ucler rectio, i which og ( 2) d ( 2) prticles of iitil d fil chels there re the differet eleetry prticles d toic uclei, llows to distiguish the possile echiss of the ivestigted rectio d to throw the echiss violtig the T-ivrice of the lyzed qutu syste. This stteet will e used for the lysis of echiss of the pperce of isotropies with differet P- d T-prities i differetil cross sectios of ucler rectios of the iry d terry fissio of orieted uclei-trgets y the cold polrized eutros. 2

3 2. THE T-INVARIANCE CONDITION FOR QUANTUM MECHANICAL SYSTEMS The T-ivrice of the qutu syste with the tie idepedet Hiltoi H, where is the totl set of sptil, spi d logous coordites of this syste, cosists [E. P. Wiger, Gottige Nchrichte, 51, 546 (192); М. L. Golderger, К. M. Wtso, Collisio theory (Wiley J. & So Ic., 1964)] i tht for y possile sttes of the ivestigted syste with the wve fuctios,t eig the solutios of Schrödiger equtio: ih, t H, t, (1) t

4 there re tie-reversed sttes with the wve fuctios,t eig the solutios of the se Schrödiger equtio (1). The wve fuctios,t re coected [E. P. Wiger, Gottige Nchrichte, 51, 546 (192); М. L. Golderger, К. M. Wtso, Collisio theory (Wiley J. & So Ic., 1964)] with the iitil wve fuctios,t s with the opertor of tie reversio Т:, t, t T, (2) T OK, () where K is the opertor of the coplex cojugtio, O is the uitry opertor stisfctory the coditio for coplex H: * OH O H. (4) For the wve fuctios of sttiory sttes stisfctory the sttiory Schrödiger equtio: 4

5 there re the tie-reversed wve fuctios equtio (5) d coected with eig solutios of the se Schrödiger H E (5) y coditio (2). Usig the forule (2, ), the trix eleet opertor Q c e represeted s where Q is the tie-reversed opertor Q: Q for ritrry 2 1 Q Q, (6) Q TQ T. (7) I this cse the tie-reversed Heriti opertors of coordite r, oet p, oritl oet L d spi s of the prticle re expressed s The opertor Q is ivrit to the tie-reversio if r r; pp; LL; s s. (8) Q Q. (9) 5

6 . THE CONDITIONS OF T-INVARINCE FOR AMPLITUDES OF MANYPARTICLES MULTISTEPS NUCLEAR REACTIONS Let us cosider the Hiltoi H for the yprticle ultistep ucler rectio s where H, H d V, H H V H V, (10) V re operturted prts of H d iterctio potetils of prticles i iitil d fil chels of the ivestigted rectio. The the operturted wve fuctios of iitil d fil chels re the solutios of Schrödiger equtios: where eergies E d E E H 0; H 0, (11) E lie o the ss surfce of ivestigted rectio: t tht E is the rectio totl eergy icluded i equtio (5). E E E, 6

7 The plitude of rectio c e expressed [М. L. Golderger, К. M. Wtso, Collisio theory (Wiley J. & So Ic., 1964); J. R. Tylor, Sctterig Theory: the Qutu Theory of Noreltivistic Sctterig (New York, 1972)] y the trix eleet T : where the rectio opertor T hs the for: T T, (12), E i 1 T = V + V H V, (1) which deostrtes the proouced depedece of this opertor i trix eleet (12) fro the structures of the wve fuctios of iitil d fil chels. Alogously the plitudes of the iverse rectio trix eleet T, of the iverse rectio opertor T y the forul:, c e expressed y the T T, (14) 7

8 where the opertor T is deterited s E i 1 T = V + V H V (15) d is differet fro the opertor T (12) y ot oly the trspositio of potetils V d V of iitil d fil chels ut d the trspositio of potetils of iteredite stges evolutio of iverse rectio i the copriso with logicl stges of iitil rectio. Usig the forule (6, 2-4) the T-ivrice coditio for the trix eleets T for the yprticle ultistep ucler rectio c e represeted [М. L. Golderger, К. M. Wtso, Collisio theory (Wiley J. & So Ic., 1964); J. R. Tylor, Sctterig Theory: the Qutu Theory of Noreltivistic Sctterig (New York, 1972)] y the forul: T T T T, (16),, 8

9 where d re tie-reversed wve fuctios d. I forul (16) the trix eleet T of iitil rectio coicides with the trix eleet T of, tie-reversed rectio. I the coo cse the trix eleet T c e represeted y the su of trix i eleets T, which re coected with oe of k relized echiss of this rectio (i = 1,, k ): k i,, i1 T T. (17) The the differetil cross sectio of the ivestigted rectio d hs the for: d k 2 k 2 k i i i j i j,,,,,,, i1 i1 i j1 T T T T T T. (18) 9

10 i The ech echis i correspods oe of two groups of trix eleets T, : T-eve trix eleets i T for echiss i=i ev d T-odd trix eleets T, odd for i, ev echiss i=i odd hvig the qulity: iev iev iodd i T, T, odd T T. (19) Usig the T-ivrice coditios (16) the followig reltios c e otied for trix eleets of the iitil d iverse rectios: iev iev iodd i T, T,,,, odd T T. (20) ev odd The the T-eve d d T-odd d syetries i the differetil cross sectio (18), defied s d d ; d d (21) ev ev odd odd,,,, d with the usge of forul (18) c e rought to fors: 10

11 d k 2 2 k i i i j i ev j, T, T, T, T, T, T, i i j d ev odd ev ev odd odd ; k i j i odd j, T, T, T, T, i j ev odd ev odd (22) The cross sectio d of the ivestigted rectio cotis the differet syetries d with coefficiets D defied [G. A. Petrov, et l., Nucl. Phys., A 502, 297 (1989); P. Jesiger et l., Nucl. Istru. Methods, A 440, 618 (2000)] s D d, d, d, d,, (2) where the sigs +/ correspod sigs of oriettios of certi vector preters coected with ivestigted syetries. Usig the T-ivrice coditio (16) it c ee uilt the logous coditio for these coefficiets: 11

12 D D (24) Let us use the represettio of rticle [F. Arsh, J. Morvcsik, G.R. Goldstei, Phys. Rev. Let., 54, 2649 (1985)], i which it ws show tht it is ipossile the vishig of y oservle i differetil cross sectios of every elstic d ielstic iry ucler rectios with the coservtio of T-ivrice, d results of rticle [S.G. Kdesky, P.V. Kostryukov, ccepted for pulictio i Bull. RAS: Phys., (2016)], i which the T- ivrice coditios hve ee geerlized for yprticle ultistep sttisticl ucler rectio with ( 2) d ( 2) prticles of iitil d fil chels. The usig the T-ivrice coditio (24) it c ee show tht the coefficiets D, d D for siilr syetries () i differetil cross sectios of iitil, d tie-reversed ucler rectios, the pperces of which re cused clerly y the uifor echis, c e represeted y the uified sclr 12

13 (pseudosclr) fuctio D, depedig fro wve vectors d spis of prticles of iitil d fil chels of ivestigted rectios d chgig it s vlues correspodigly to forul (8) for the trsitio fro iitil rectio to tiereversed ucler rectio:, ;, ;, ;, D D k s k s D D k s k s. (25),, The the T-ivrice coditio (24) rigs to coditio for the coefficiets D, ;, D, ;, D : k s k s k s k s. (26) Aog the coefficiets D it c e rked T-eve D ev d T-odd D odd coefficiets: ev ev odd odd D D ; D D, (27),,,, for which T-ivrice coditios (26) re represeted y the fors: D D odd ev ev k, s; k, s D k, s; k, s, odd k s k s D k s k s, ;,, ;,. (28) 1

14 The depedece of the fuctios ev odd D d D fro wve vectors d spis of prticles c e foud (experietlly or theoreticlly) for iitil rectio d with the usge of the T-ivrice coditio (28) is used for testig of echiss of the pperce of isotropies with differet P- d T-prities i differetil cross sectios of differet ucler rectios stisfctory the T-ivrice of ucler syste. 14

15 4. THE MECHANISMS OF FORMATION OF DIFFERENT ASYMMETRIES IN DIFFERENTIAL CROSS SECTIONS OF BINARY AND TERNARY FISSION OF ORIENTED TARGET-NUCLEI BY POLARIZED NEUTRONS. I differetil cross sectios of iry d terry fissio of o-orieted trget-uclei y cold polrized eutro the syetries coefficiet, ;, D k s k s (25) of types k, k, s, k, s, k, k, k k, s k,,,,, s k k, where k, k re wve vectors of goig i eutro, light fissio frget d third prticle; s is the vector of the eutro spi, were discovered [G.V. Dily et l., Lett. JETP, 26, 197 (1977); V.N. Adreev et l., Lett. JETP, 28, 58 (1978); A.K. Petukhov et l, Lett. JETP, k 15

16 0, 24 (1979); V.A. Ves et l, Lett. JETP, 1, 704 (1980); G. A. Petrov, et l., Nucl. Phys., A 502, 297 (1989); P. Jesiger et l., Nucl. Istru. Methods, A 440, 618 (2000); P. Jesiger, A. Kötzle, F. Göeewie, Phys. Ato. Nucl., 65, 60 (2002); F. Göeewie et l., Phys. Lett., B 652, 1 (2007); G.V. Dily et l., i Proceedig of the ISINN-15, JIRN, Du, 111 (2008); G.V. Dily et l., Phys. Ato. Nucl., 7, 1116 (2010)]. I the se tie i theoreticl rticles [O.P. Sushkov, V.V. Flu, UPN, 16, (1982); V.E. Bukov, V.P. Gudkov, Nucl. Phys, A 401, 2 (198); S.G. Kdesky, Phys. Ato. Nucl., 65, 190 (2002); V.E. Bukov, F. Göeewie, Phys. Ato. Nucl., 65, 206 (2002); V.E. Bukov, S.G. Kdesky, Phys. Ato. Nucl., 66, 1846 (200); S.G. Kdesky, Phys. Ato. Nucl., 67, 170 (2004); S.G. Kdesky, V.E. Bukov, S.S. Kdesky, Phys. Ato. Nucl., 74, 555 (2010); S.G. Kdesky, V.E. Bukov, L.V. Titov, Phys. Ato. Nucl., 78, 708 (2015)] the differet echiss of pperce of these syetries were proposed. P-eve T-eve syetry k, k, P-eve T-odd 16

17 syetry s, k, k d P-odd T-eve syetries s, k, s k pper i differetil cross sectios of lyzed rectios y tkig ito ccout the echiss coected with the iterferece of fissio plitudes of s- d p-eutro resoces of copoud uclei. P-eve T-eve syetry k k re coected with the, echiss, sed o the iterferece of the se d differet s-eutro resoces. Used echiss of the pperce of ll cosidered ove syetries d too lyzed theoreticlly syetries Ik, I, k, k, Ik,,,,,, I k k, where I is the polrizility vector of trget-ucleus, stisfctory the T-ivrice coditios (28). I the se tie syetry,, syetry,, s k k d theoreticlly ivestigted I k k cused y the ifluece of Coriolis iterctio o the gulr distriutios of third prticle does t stisfctory the T-ivrice coditio (28) for the echis of siulteous flights fro fissile copoud ucleus third 17

18 prticle d fissio frgets. Oly for the echis of sequetil flights fro fissile copoud ucleus third prticle d fissio frgets, which is coected with the o-evportio echis [O. Tiur, T. Fliessch, Z. Phys., A 28, 475 (1987); S.G. Kdesky, L.V. Titov, A.O. Bulychev, Phys. Ato. Nucl., 78, 672 (2015)] of third prticle flight cused y the oditicl otio of fissile ucleus er it s scissio poit, stisfctory of the T-ivrice coditio (28). It is very iterestig to lyze the echiss of pperce of ew syetries I, s, k, I, s, k, I, s, k, k, I, s, k, k,,,, I s k k for iry d terry fissio of orieted ucleus-trget y cold polrized eutros. These syetries stisfy the T-ivrice coditios (28) oly for echiss tkig ito ccout the iterferece eutros resoces sttes with differet vlues of it s spis d correspodig to sequetil flights of third prticles d fissio frgets for terry fissio. 18

19 Thk you for ttetio 19

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