Le Noyau de l'atome. Master 2 - NPAC 2009/10 Noyaux Particules Astroparticules Cosmologie. Marcella Grasso IPN-Orsay

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1 Master 2 - PAC 2009/10 oyaux Particules Astroparticules Cosmologie Le oyau de l'atome Marcella Grasso IP-Orsay grasso@ipno.in2p3.fr Miguel Marqu es LPC-Caen marques@lpccaen.in2p3.fr

2 Master 2 - PAC 2009/10 oyaux Particules Astroparticules Cosmologie Le oyau de l'atome ITRODUCTIO FORC UCLAIR LABORATOIR SYSTMS A CORPS CHAMP MOY RACTIOS LIMITS D STABILIT SUPRFLUIDIT ASTROPHYSIQU SYMTRIS

3 TH STRUCTUR OF MATTR 10,000, cm 3 Iron 10,000 atoms atom : e(-) & nucleus (+)? 1 cm 3 Iron = 7.9 g 85,000,000,000,000,000,000,000 atoms! % of matter is empty! 1 cm 3 of nuclei = 300 million tons! nucleus : p(+) & n(0) PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (1) L P C C A

$TOO MAY \LMTS" PAC/2009/\Le oyau de$

4 TOO MAY \LMTS" PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (2) L P C C A

5 HIRARCHY I ATOMIC STRUCTUR Smaller constituents have proved to be composite systems: end of XIX, matter composed of atoms but 100 elements showing periodical properties... beginning of XX, electron and nucleus 1932, discovery of the neutron! The building blocks : e p + n 0 (+ν) 1950/60s, accelerators produce 100 hadrons! the \hadronic zoo" can be classied in groups... All known hadrons are combinations of 2 or 3 quarks! leptons+quarks : < m, no excited states uclear physics has not profited much from analogy. The reason seems to be that the nucleus is the domain of new and unfamiliar forces, for which men have not yet developed an intuitive feeling.. [Scientific American (1962)] PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (3) L P C C A

6 TH BUILDIG BLOCKS LCTRO In 1897, Thomson produces beams of particles in discharge tubes : by deecting them (υ, M/Q) a universal constituent of matter! then measures Q M = 511 kev/c 2 PROTO In 1911, Rutherford nds a central Coulomb eld in the atom caused by a massive, positively charged nucleus... Bombarding nuclei with α's : He 17 O + p he observes positively charged particles with a very long range! Hydrogen nuclei? elementary constituent of nuclei! UTRO A \neutral radiation" had been observed but not understood... In 1932, Chadwick irradiates Beryllium with α's from Polonium source : radiation collides with several nuclei that recoil in ionisation chamber : mass similar to that of the proton new constituent, the \neutron"! BIDIG Once the constituents known, the forces holding them could be investigated... stronger than atomic forces : need energetic α's to break up mass defect of the order of 1% : experimental proof of = Mc 2! PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (4) L P C C A

7 PROTOS + UTROS = UCLI The atomic number : Z protons in the nucleus Q = Ze, with e p + e e < e Moseley's law : K α -line (Z 1) 2 The mass number : A = Z + nucleons form nuclei A Z X same A, isobars same, isotones same Z, isotopes (of element X) Binding from atomic masses? B(, Z) = ZM1 H + M n M(, Z) r r M υ 2 = M Q = M υ Q B Reference mass : 1u = M12 C/12 = MeV/c 2 uclear reactions : 1 H(n, γ) 2 H B = M n + M1 H M2 H where M1 H = M p +m e... ( 13.6 ev) = γ + 2 γ 2M2 H = MeV PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (5) L P C C A

8 MASSS I TH SOLAR SYSTM Relative abundance in terrestrial, lunar and meteoritic probes : Local deviations, for example : 2 H, He right after Big Bang up to Fe by fusion in stars heavier nuclei in supernovae Xe isotopes in drill core found at 10 km depth (top) and in the arth's atmosphere (bottom)... Xe isotopes in the core from. spontaneous ssion of Uranium! PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (6) L P C C A

9 BIDIG RGY PR UCLO For most nuclei it is about 8 MeV : short range force, about d saturation, ρ /fm 3 about 1% of nuclear mass Slow decrease toward Uranium : spontaneous/induced ssion? nuclear power plants \atomic" bomb Strong rise toward Iron : fusion in stars fusion on arth? ITR H-bomb Liquid Drop analogy : overall very good description! pairing and shells? PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (7) L P C C A

10 TH LIQUID DROP MODL Semi-empirical mass formula : M(, Z) = M n + ZM p B(, Z) a v A VOLUM a s A 2/3 SURFAC a c Z 2 /A 1/3 COULOMB a a ( Z) 2 /A ASYMMTRY 11.2 ± δ/a 1/2 PAIRIG [MeV] volume : strong force dominates binding energy A, not to A(A 1) A 2 surface : fewer neighbors nuclear surface R 2 Coulomb : electrical repulsion calculated as 3 Z(Z 1)α c/r 5 asymmetry : compensate repulsion surplus of neutrons asymmetry increases with A pairing : nucleon coupling pp and nn pairs smaller overlap in larger nuclei PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (8) L P C C A

$n, Z z) + M(n, z) n = z = 2 : α decay (n+z) A/2 : spontaneous ssion PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (9) L P C C A$

11 UCLAR STABILITY Particle stability } M(, Z) < min{ M(ni, z i ) p n : β decay excited states : γ decay Particle instability M(, Z) > M( n, Z z) + M(n, z) n = z = 2 : α decay (n+z) A/2 : spontaneous ssion PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (9) L P C C A

12 BTA DCAY M(A, Z) = αa βz + γz 2 ± δ/a 1/2 β decay n p + e + ν e M(A, Z) > M(A, Z + 1) β + decay p n + e + + ν e M(A, Z) > M(A, Z 1) + 2m e e capture p + e n + ν e M(A, Z) > M(A, Z 1) + ε. ( of daughter atomic shell) PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (10) L P C C A

13 TH DCAY OF K40 Radioactive decay : 40 K : all 3 β-decays! probability per unit time λ lifetime τ, half-life t 1/2 activity A (decays per unit time) τ = 1/λ t 1/2 = ln 2/λ A(t) = λ (t) = λ 0 e λt 1 Bq = 1 decay/s β decay : τ : few ms to years! 1/τ 5 decay of free neutron : = 780 kev, τ = ± 1.9 s no 2 neighboring isobars β-stable... C more energy (2m e ε) available 40 K is 0.01% of natural K : K + signal transmitter in nervous system 16% of human radiation exposure! 70 kg human = 4,400 decays/s! K-Ar dating method for rocks PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (11) L P C C A

14 ALPHA DCAY α tunnelling : T r e 2 2m V r T = e 2 G the Gamow factor : G = 1 r1 R 2m V dr π 2(Z 2) α/β Z/ τ : few ns to years! λ = w(α) υ 0 2R e 2G PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (12) L P C C A

15 UCLAR FISSIO Potential during spontaneous ssion : s = a s A [1 2/3 + 2 ] 5 ε2 + Z 2 [ c = a c 1 1 ] 5 ε2 + A 1/3 small deformation ε changes by : ε2 ] [2a s A 2/3 a c Z 2 A 1/3 5 Deform sphere into ellipsoid : ssion barrier disappears for : Z 2 A 2a s a c 48 about Z > 114 and A > a = R (1+ε) b = R (1 ε/2) } ab 2 R 3 Induced ssion : Z 92 : barrier 6 MeV n capture by odd nuclei +δ! 235 U (not 238 U), 233 Th, 239 Pu... PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (13) L P C C A

16 TH FRMI GAS MODL : UCLI ach nucleon feels the superposition of the potentials of all other nucleons : Heavier nuclei have surplus of neutrons : equal Fermi levels V C (Z 1)/R binding energy for Z? kin = pf 0 kin p 2 dp pf 0 p2 dp = 3/5 p2 F 2M 20 MeV states available to a nucleon: dn = 4πp2 dp (2π ) 3 V pf 0 dn = V p3 F 6π 2 3 = Z = V p F 3 3π 2 3 V = 4/3 πr 3 = 4/3 πr 3 0 A } R n = R p p n,p Z = = A/2 F 250 MeV/c kin (, Z) = n + Z p = 3 [ (p n F 10M )2 + Z(p p F )2] [ ]2 = 3 2 9π 3 5/3 + Z 5/3 10Mr0 2 4 A 2/3 = Mr 2 0 [ 9π 8 ]2 3 [ A + 5 ( Z) 2 9 A volume and asymmetry terms! ] + PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (14) L P C C A

17 TH FRMI GAS MODL : STARS A huge liquid, neutral drop : B/A (a v a a ) G m2 n r 0 A 2/3 (A min ) B>0 depends on a a!!! a a [MeV] A min R [km] M/M A 1/ roughly a neutron star... Supernova explosion (M = 1.5 M ) : 56 Fe + 26 e 56 n + 26 ν e cold neutron gas ( = ) : Fermi pressure vs gravity! [ ]1 9π 3 p F = 4 R 3 2 [ 9π kin / = 10M n R 2 4 pot / = 3 5 G M2 n R the star is in equilibrium if : d dr / = 0 R = 12 km R = 2 (9π/4) 2/3 GM 3 n 1/3 ρ = 0.25 n/fm 3 = 1.5 ρ 0 ρ can be higher : Λ, quarks... ]2 3 PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (15) L P C C A

18 \MARKD" UCLOS : HYPRUCLI The system of nucleons in nuclei is small enough to posses discrete energy levels with l = 0, 1, 2,... : at T = 0 all states are occupied can only swap places (unobservable) : looks like each is in (, l) state! if only we could \mark" nucleons... Introduce hyperon as a probe! Λ [uds] : τ = s strangeness exchange reactions : K + A Λ A + π ( ) K [ūs] + n [udd] Λ [uds] + π [ūd] p K 500 MeV/c + θ π = 0 : no momentum transfer to Λ A PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (16) L P C C A

19 HYPROS I UCLI Systematic research in heavier nuclei : π + + A Λ A + K + If Λ remains inside nucleus ( 12 Λ C) : B Λ B n + ( π K ) + (M Λ M n ) with neutron at Fermi level : B n S n peaks in B Λ spectrum ( π ) : B Λ = 0 : Λ stays in 1p B Λ 11 MeV : Λ may go to 1s! B Λ < 0 : for deeper lying n Λ hyperons occupy discrete levels lines : V 0 = 30 MeV and R = r 0 A 1/3! Λ moves as a free particle in A... PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (17) L P C C A

20 TH SHLL MODL Λ A nucleons occupy energy levels : like electrons in the nucleus' eld! but nucleons move in \their" eld... lectrons are ordered in \shells", groups of nearby energy levels : compact nuclei with certain /Z 2, 8, 20, 28, 50, 82, 126 magic numbers a lot of energy needed in order to : extract a neutron/proton (S n/p ) or excite them (like noble gases) exceptionally stable doubly magic nuclei : 4 2 He O Ca Ca Pb 126 numbers explained by SHLL MODL R nl (r) Y m l (θ, φ) { n = 1, 2, 3, 4,... l = s, p, d, f, g,... short-range force V follows ρ(r) : Gaussian (HO) for light nuclei Fermi (WS) for heavy nuclei... PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (18) L P C C A

$0 2 5 H 4 (neutrons) 6 9 He 8 10 12 1 16 B 2 3 4 5 7 6 Z (protons) PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M.$

21 XOTIC UCLI ] gs = min[ M(ni, z i ) M(, Z) gs [MeV] 10 5 Z= Z (protons) (neutrons) H 4 (neutrons) 6 9 He B Z (protons) PAC/2009/\Le oyau de l'atome" CHAPTR 1 F.M. Marqu es (19) L P C C A

Fundamental Forces. Range Carrier Observed? Strength. Gravity Infinite Graviton No. Weak 10-6 Nuclear W+ W- Z Yes (1983)

Fundamental Forces. Range Carrier Observed? Strength. Gravity Infinite Graviton No. Weak 10-6 Nuclear W+ W- Z Yes (1983) Fundamental Forces Force Relative Strength Range Carrier Observed? Gravity 10-39 Infinite Graviton No Weak 10-6 Nuclear W+ W- Z Yes (1983) Electromagnetic 10-2 Infinite Photon Yes (1923) Strong 1 Nuclear