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## Beta Decay – General Principles

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**Beta Decay – General Principles**• Paul Mantica • Lecture 1 • Euroschool for Exotic Beams • Leuven, Belgium - 2009**Beta Decay of Exotic Nuclei:Science Opportunities**Beta decay properties of unstable nuclei far from stability can provide valuable insight into nuclear shell structure and nuclear deformation changes toward the drip lines. Precise beta-decay half-lives, end point energies, and branching ratios to unbound states are crucial nuclear physics input parameters for network calculations of the astrophysical rapid neutron capture process. The selective method of beta decay, in combination with spectroscopic measurements of gamma-rays and neutrons, will open new opportunities to study, for example: • Gamow-Teller strength in N~Z nuclei to 100Sn • Persistence of shell gaps in extreme neutron-rich nuclei (60Ca, 128Pd) • r-process waiting point nuclei along N=82 (124Mo, 123Nb, …) and N=126 (195Tm, 194Er …) • E(4+)/E(2+) and phase transitions away from stability (122Pd, 90Ge, 148Xe, …) • and others …**Beta Decay of Exotic Nuclei:Application of Fast Beams**Significant progress has been made in the measurement of beta-decay properties of exotic nuclei, attributed directly to particle-detection techniques employed with fast beams. • Advantage of fast beams: • Can correlate implantations and decays event-by-event • ID of decay parent • suitable for cocktail beams • crucial for systematic investigations • reduction in background and increased sensitivity • half-life: few per day • beta-neutron: few per hour • beta-gamma: few per minute**Beta Decay of Exotic Nuclei:Reach Across the Nuclear Chart**Beta decay half-lives All waiting points along N=82 and many along N=126 will be established First 2+ energies Major advance in characterizing the systematic variation of E(2+) and E(4+)/E(2+) with increasing neutron number**Beta Decay of Exotic Nuclei:Experimental Needs and**Observables BCS SeGA • Needs: • Fast beams via fragmentation or fission • Highly-segmented implantation detector • Overall implantation rate < 500 s-1 • high resolution separator • Digital readout (dedicated electronics) • Ancillary detectors • electrons, neutrons, photons, etc. • Floor space: 3 m x 3 m x 3 m • Observables: • Half-lives • Q values (masses) • Absolute branching ratios • Excited states in daughter nuclei • Microsecond isomers • excited states in parent NERO**Types of Beta Decay**b- decay 204Bi EC decay 204Pb EC/b+ decay Proton number b- decay 204Tl b+decay Neutron number**delayed neutron**branching beta half-lives delayed gamma rays Beta Decay Observables isomer half-lives isomeric gamma rays T1/2 g T1/2 b– Pn n g b– Beta endpoint energy Qb b– g g g absolute beta branching**Beta Decay Energetics**A=204 Mass Chain 204Bi 204Tl Mass = f1(A)Z2+f2(A)Z+f3(A)-d 204Pb**Beta Decay Endpoint Energy**b- decay EC decay b+decay**Beta Energy Spectrum**Decay energy is shared between the electron and the neutrino ~1/3 Eb(max) Energy spectrum is for the positron is continuous up to the endpoint energy**Radioactive Decay Kinetics**Radioactive decay and growth as the form of a first order rate law Nt=Noe-lt No is the initial number of nuclei Nt is the number of nuclei at time t e is a mathematical constant 2.7182818284 l is the decay constant The characteristic rate of a radioactive decay is conveniently given in terms of the half life t1/2=ln 2/l 0.693/l The half life is the average time required to reduce the initial number of nuclei by a factor of 2**Decay Rates for Beta Emission:Energetics**There are a wide range of beta decay half lifes: In general, large decay energies are associated with very short beta-decay half-lives Rate is proportional to Decay Energy (E0) and Proton Number (Z)**Decay Rates for Beta EmissionInitial and Final States**However, beta-decay half-lives also depend strongly on the properties of the initial and final states involved in the decay Beta transition strength is expressed as a product of the energy factor times the half-life (log f0t values).**Allowed Beta Decay**• Allowed transitions come in two types: • Fermi (D=0) and Gamow-Teller (D= 1). • Relative orientation of angular momentum vectors for the emitted neutrino and fast electron • Log fot is an expression of the transition strength that considers the energy of decay (fovalue) and the time for decay (t), where t is the partial half-life for the decay. log fot= log fo+ log t log t is the logarithm of the partial half-life of the beta decay t = [t1/2]/branch (in seconds) SuperallowedFermi Decay Allowed Decay parity DJ=0 Dp=no log ft ~ 3.5 DJ=0,1 Dp=no log ft ~ 4-7 p=(-1)**Gross Beta Decay Theory**T1/2 a (Qb - C)-b a = 2740 s b = 4.5 Qb = b endpoint energy C = cutoff energy (pairing gap in daughter) Sb(E) is the beta-strength function f is the Fermi function R is the nuclear radius Qb is the endpoint energy Ei is the energy of the final state • Gross b decay results overestimate the half-lives of the most neutron-rich isotopes • b-decay rate to low-energy states in daughter underestimated Tachibana et al., Prog. Theor. Phys. 84, 641 (1990) Pfeiffer, Kratz and Möller, Prog. Nucl. Energy 41, 39 (2002)**Gross Theory vs. Experiment**Note that: Fermi function is dominated by the phase space factor (Qb-Ei)5 The average error increases as T1/2 increases Inclusion of first forbidden decay (ff) improves average error for longer T1/2 values Uncertainty in masses far from stability does not dramatically impact T1/2, since relative error does not increase rapidly (Qb is large) Mölleret al., PRC 67, 055802 (2003)**Beta Decay – Execution at Fast Beam Facilities**• Paul Mantica • Lecture 2 • Euroschool for Exotic Beams • Leuven, Belgium - 2009**National Superconducting Cyclotron Laboratory**• 30 Faculty • 19 Experimental • 7 Theory • 4 Accelerator Physics • 60 Graduate Students • 50 Undergraduate Students • 700 member Users Group • Selected to design and establish Facility for Rare Isotope Beams (FRIB) … a world leader in rare isotope research and education Biochemistry NSCL Chemistry Law school**Fast-moving projectile is abraded, resulting projectile-like**fragment travels with a velocity similar to initial projectile Produce many isotopes below the initial projectile A and Z, both stable and radioactive Separation does not depend on the chemical properties of the isotopes DE TOF Projectile Fragmentation 78Kr Fragmentation @ 70 MeV/A Each fragment can be uniquely identified using time-of-flight, energy-loss, and magnetic rigidity**Rare Isotope Beam Production**Primary stable atoms are ionized in an ECR source and injected into the accelerating system composed of the coupled K500 and K1200 superconducting cyclotrons K500 A1900 K1200 The fast, stable beam is then impinged on a target at the object of the A1900 separator**Rare Isotope Beam Selection**The A1900 Fragment Separator is used to select the rare isotope of interest from unwanted fragmentation products ECR ion sources • Dp/p = 5% max • Br = 6.0 Tm max • 8 msr solid angle • 35 m in length K500 A1900 K1200 target wedge focal plane Production of 78Ni from 140 MeV/A 86Kr Morrissey et al., NIM B 204, 90 (2003)**Backplate**PINS Planer Ge NSCL Beta Counting System (BCS) Implantation detector: 1 each MSL type BB1-1000 4 cm x 4 cm active area 1 mm thick 40 1-mm strips in x and y Calorimeter: 6 each MSL type W 5 cm active area 1 mm thick 16 strips in one dimension Prisciandaroet al., NIM A 505, 140 (2003)**Heavy Charged Particles**Primary interaction is via the electromagnetic interaction between the positive charge of the heavy ion and the negative charge of the orbital electrons within the detection medium. The maximum energy that can be transferred is 4Eme/m Where m and E are the particle mass and energy, respectively, and me is the electron mass. Since me is much smaller than the incoming particle mass, the energy transfer is small. primary particle loses its energy over MANY interactions produce many excited atoms or ion pairs in the detector material**Stopping Power**The linear stopping power for charged particles is given as Through the Bethe formula, the linear stopping power is a function of the atomic number of the stopping material (Z) and the ion charge (q) and velocity (b=v/c) of the incident particle Range can be obtained by integrating the energy loss rate along the path of the ion: -dE dx Distance of penetration**Range of Projectile Fragments in Silicon**Stopping power scales with ion mass, charge and energy: Scaling can be extended to range calculations: http://www.physics.nist.gov/PhysRefData/Star/Text/ASTAR.html**Practical Calculation:Range of 78Ni in Silicon**The range of 100 MeV/A 78Ni in Si can be scaled from the range of 100 MeV/A alpha particles.**Fast Electrons vs. Heavy Ions**Fast electrons lose energy at a lower rate and follow a more torturous path through absorbing materials. This can be attributed to the low ion charge (z = 1) and low mass of the electron. Fast electrons can also lose energy through radiative processes S (1/v)2 NZ (electronic) S NEZ2 (radiative) Therefore the radiative loses are most important for high energy electrons where the absorbing material has a large atomic number.**Range of Fast Electrons in Silicon**The range of a 10 MeV beta particle in Si is 5.8 g/cm2 r(Si) = 2.33 g/cm3 Therefore, the amount of Si required to fully stop a 10 MeV beta particle is ~ 2.5 cm! http://physics.nist.gov/PhysRefData/Star/Text/ESTAR.html**Signal Processing for Heavy Ions and Betas in a Single**Silicon Detector Challenge: beta DE ~ 100’s of keV beam E ~ 1’s of GeV CPA16 dual gain preamp from MultiChannel Systems: 16 channels, 50W input impedance, 2V output, ~350 ns rise time. Low gain: High gain: 0.03 V/pC 2.0 V/pC output to ADCs output to Pico Systems 16 ch shaper**PID**PID NIM Trigger CAMAC Shapers Digitized waveform: short-lived proton decay of 145Tm VME Readout Grzywacz NIMB 204, 649 (2003) XIA PIXE-16 660 channels commissioned and in use with SeGA BCS Electronics Conventional BCS Electronics: Block Diagram Digitization**A0**Bulk Activity Measurements Implant activity into a stopper material for time timplant. Cease implantation and observe decay for time tdecay. If necessary, introduce a “clean” stopper material and repeat. For deposit of a single isotope: A=Nl For example shown: timplant = tdecay=4t1/2**Time Correlation of Implantations and Charged-Particle**Decays • Correlations between an implantation event and subsequent b-decay events are done based on position and time • Information regarding the particle ID is carried over to a correlated decay event, therefore, b decays are unambiguously identified • Both prompt and delayed g rays can also be unambiguously assigned • Decay curves are generated from the difference in absolute times between and implantation and correlated decay event The high pixel density of the DSSD and low implantation rates (less than 200 ions/second) are essential to reduce probabilities for incorrect correlations b Azq+ Implantation Decay Absolute time Position (x,y) Energy loss and time of flight Fragment total kinetic energy Gate the g-array ADCs for 20 ms Absolute time Position (x,y) Energy of outgoing particle Gate the g-array ADCs for 20 ms**Bateman Equations**The Bateman equations provide a means for analyzing a chain of many successive radioactive decays. Special assumption: At t=0, only parent is present.**Consecutive First-Order Decays**For nuclei far from stability, the typical condition is that parent This condition is the non-equilibrium case for radioactive decay, and, for a three-generation decay, the number of grand-daughter nuclei will eventually equal the initial number of parent nuclei (assuming the daughter and grand-daughter are not produced directly) daughter grand-daughter**Low Counting Statistics and the Likelihood Function**Background 1 decay observed: Decay Functions Efficiency 2 decays observed: 10 scenarios → 3 decays observed: 20 scenarios → constant Pereira et al., PRC 79, 035806 (2009)**Background and Maximum Likelihood**Background rate was determined uniquely for each 100Sn decay by considering the entire time-lapsed history of implantations into the DSSD Determination of the 100Sn half-life came from maximizing the likelihood function, considering also those implantation events that were not correlated with a decay The simulation below shows the close matching between simulated and observed decay rate. Since N0 depends on l1 itself, an iterative process is used to maximize the function**Beta Decay – Neutron-Deficient Nuclei**• Paul Mantica • Lecture 3 • Euroschool for Exotic Beams • Leuven, Belgium - 2009**rp-Process Nucleosynthesis**• Demonstrated burst conditions [1] • T=1.5-2 GK • r ~ 106g/cm3 • lb~ 0.6 s-1 • lp ~ 10,000 s-1 Termination point Reactions of rp-process • Parameters: • b-decay rates • (a,g),(p, g) rates • Masses Feeding from (a,p)-process Schatz et al., NPA 688, 150c (2001)**Challenges with Neutron-Deficient Nuclei**Selected Fragment: Mo-84 Projectile: 124Xe48+ at 140 MeV/A Target: 9Be, 305 mg/cm2 Acceptance: 1% Wedge: 27Al, 180 mg/cm2 Not only is the production of 84Mo overwhelmed by peak production of lighter isotones, but the low-momentum tails of the more prolifically produced, near stable isotopes also dominate the total yield, even with use of a wedge degrader. Rate in pps/pnA from LISE++**RF Fragment Separator**The RF Fragment Separator was commissioned at NSCL in April 2007. The first beta-decay campaign to study neutron-deficient nuclei was initiated October 2007. Operating principle:Beam species that have similar Br differ in TOF. Beam Packets**84Mo Production and RFFS Performance**V = 0 kV Y slits = 50 mm Ibeam = 0.8 pnA 83 s-1 over DSSD V = 47 kV Y slits = 10 mm Ibeam = 10 pnA 0.5 s-1 over DSSD * Rates relative to 84Mo, 5×10-4pps/pnA ** particles/s-pnA PID are normalized to same number of 80Y implantations**Half-life of 84Mo**84Mo is a waiting point along the rp-process. The re-measured half-life was found to be more than 1s shorter than the previous value, accelerating mass processing along the rp-process pathway. Previous T1/2 = 3.7 (+1.0, -0.8) s Decay curve for 84Mo T1/2 = 2.2±0.2 s Half-lives of even-even N=Z nuclei compared with theory Stoker et al., PRC 79, 015803 (2009)**Correlated 84Mo Decays**Maximum likelihood analysis requires extraction of correlated beta decays. Correlations were defined for 84Mo by limiting the time window for correlations to less than 20 s after an implantation. In addition, beta decays that occurred in the same pixel as the implantation, or any of the four nearest-neighbor pixels, were considered. Three generations of decays were taken into account to generate the likelihood function. The log t between a given 84Mo implantation and the subsequent one, two, and three beta correlations are shown to the right. The half-life value from the maximum likelihood analysis was consistent with that extracted from the decay curve fit.**Impact of the Shorter Half-Life of 84Mo**The order of magnitude uncertainty in the final 84Sr abundance has been reduced to less than a factor of 2 with the new half-life. A=84 abundances Previous uncertainty bounded by divergent theoretical T1/2 predictions (0.8 s lower bound; 6.0 s upper bound) Schatz et al., Phys. Rep. 294, 167 (1998)**Delayed Proton Emission**For nuclei with Z > N, the proton drip line is located where the proton separation energy equals zero Neutron-deficient nuclei near the proton drip line typically have large QEC values, and beta decay can directly populate proton unbound states. The “delayed” protons will be emitted with the apparent half-life of the beta decay. Sp**Statistical Treatment of Delayed Proton Emission**When the level density of the proton unbound states in the daughter is smaller than the resolution of the particle detector, the individual protons cannot be distinguished. A statistical treatment of the proton spectrum can then be applied. Need GT matrix element <s>, level densities r, and transmission coefficient for proton decay Tℓ Huang et al.,PRC 59, 2402 (1999)**Delayed Protons from 81Zr Decay**Delayed gamma rays Delayed protons**Termination of the rp Process**Known ground state alpha emitters among the neutron-deficient Te isotopes result in the theoretical termination of the rp process with the Sn-Sb-Te cycle. Decay data in the vicinity of the doubly-magic nucleus 100Sn is critical to the characterization of the nuclear structure effects in this region of the nuclear chart. Sn-Sb-Te cycle. The solid lines indicate reaction flows of more than 10%. Schatz et al.,PRL 86 3471 (2001)

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