Lifetime values for alpha decay in even-even nuclei with $Z=84-98$ and $N=128-152$ have been calculated in the superasymmetric fission model. The interaction between the alpha particle and the daughter nucleus has been formed in the double folding approach using a density dependent NN interaction. The densities have been obtained using the Relativistic Mean Field formalism. The spectroscopic factors for the decays have been deduced and are shown to vary smoothly as a function of effective numbers of valence nucleons, $N_p$ and $N_n$ chosen with a suitable core. The implication of such a smooth behaviour has been discussed.
The alpha-decay half-lives and the alpha-capture cross-sections are evaluated in the framework of unified model for alpha-decay and alpha-capture. In the framework of this model the alpha-decay and alpha-capture are considered as penetration of the alpha-particle through the potential barrier formed by nuclear, Coulomb and centrifugal interactions between alpha-particle and nucleus. The spins and the parities of parent and daughter nuclei as well as the quadrupole and hexadecapole deformations of daughter nuclei are taken into account for evaluation of the alpha-decay half-lives. The alpha-dec…
Spontaneous fission and alpha decay are the main decay modes for superheavy nuclei. The superheavy nuclei which have small alpha decay half-life compared to spontaneous fission half-life will survive fission and can be detected in the laboratory through alpha decay. We have studied the alpha decay half-life and spontaneous half-life of some superheavy elements in the atomic range Z = 100-130. Spontaneous fission half-lives of superheavy nuclei have been calculated using the phenomenological formula and the alpha decay half-lives using Viola-Seaborg-Sobiczewski formula (Sobiczewski et al. 1989)…
The set of parameters for alpha-nucleus potential is derived by using the data for both the alpha-decay half-lives and the fusion cross-sections around the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated alpha-decay half-lives and the fusion cross-sections agreed well with the data. Fusion reactions between alpha-particle and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.
The updated data for the ground-state-to-ground-state alpha-transition half-lives in 401 nuclei and the alpha capture cross sections of 40Ca, 44Ca, 59Co, 208Pb and 209Bi are well described in the framework of the unified model for alpha-decay and alpha-capture. The updated values of the alpha decay half-lives, the binding energies of nuclei, the spins of parent and daughter nuclei, and the surface deformation parameters are used for the reevaluation of the model parameters. The data for the ground-state-to-ground-state alpha-decay half-lives are also well described by the empirical relationshi…
We study the influence of proton-neutron (p-n) correlations on alpha-decay width. It is shown from the analysis of alpha Q values that the p-n correlations increase the penetration of the alpha particle through the Coulomb barrier in the treatment following Gamow's formalism, and enlarges the total alpha-decay width significantly. In particular, the isoscalar p-n interactions play an essential role in enlarging the alpha-decay width. The so-called "alpha-condensate" in Z > 84 isotopes are related to the strong p-n correlations.
We have constructed new proximity function particularly for interaction between two superheavy nuclei based on the experimental alpha decay half-lives. The new proximity function is used to produce the alpha decay half-lives of superheavy nuclei whose experimental values are known. The new proximity function produces the alpha decay half-lives close to the experiments. Hence we can conclude that the new proximity function can be used to study the interaction between two superheavy nuclei.
The competition between alpha- and beta+/EC-decay modes is studied systematically in nuclei along the alpha-decay chains following the synthesis of superheavy nuclei with Z = 119 and Z = 120. A microscopic approach based on deformed self-consistent Hartree-Fock mean-field calculations with Skyrme forces and pairing correlations is used to describe the beta+ and electron capture weak decays, whereas the alpha-decay is estimated from existing phenomenological expressions. It is shown that alpha-decay is in most cases the dominant decay mode, but interesting instances are identified where the hal…
Systematic alpha-nucleus folding potentials are used to analyze alpha-decay half-lives of superheavy nuclei. Preformation factors of about several per cent are found for all nuclei under study. The systematic behavior of the preformation factors and the volume integrals of the potentials allows to predict alpha-decay energies and half-lives for unknown nuclei. Shell closures can be determined from measured alpha-decay energies using the discontinuity of the volume integral at shell closures. For the first time a double shell closure is predicted for Z_magic = 132, N_magic = 194, and A_magic = …
Using an alpha decay level scheme, an explanation for the fine structure in odd nuclei is evidenced by taking into account the radial and rotational couplings between the unpaired nucleon and the core of the decaying system. It is stated that the experimental behavior of the alpha decay fine structure phenomenon is directed by the dynamical characteristics of the system.
Alpha and cluster decay half lives for W isotopes in the range between 2p drip line and beta stability line are studied. The sensitivity of different Skyrme parametrizations in predicting the alpha decay and probable cluster decay modes from W isotopes have been analysed. The half lives are calculated using UDL. Predicted half lives are compared with ELDM and also with available experimental values. The study also revealed the role of neutron shell closure in cluster decay process.
The process of alpha disintegration has been studied theoretically in the framework of a microscopic superasymmetric fission model (MSAFM). The nuclear interaction potential required for the alpha decay process has been calculated by folding in the density distribution functions of the alpha nucleus and the daughter nucleus with a realistic effective interaction. The nuclear microscopic alpha-nucleus potential thus obtained has been used along with the Coulomb interaction potential to calculate the action integral within the WKB approximation. This subsequently results in a parameter free calc…
The interaction potential between the alpha particle and the deformed parent nucleus was used for description of the decay of superheavy nuclei. It consists of centrifugal, nuclear and Coulomb parts suitably modified for deformed nuclei. The significant effect of various shapes of barriers obtained for deformed parent nuclei on calculated alpha half-life times were shown. The finally calculated half-life times due to the spontaneous alpha decay for superheavy elements were compared with the results obtained from other models and the experimental data.
G. Gamow's alpha-decay theory (1928), although successful, has a wrong phenomenological argument that an alpha-particle inside a radioactive nucleus moves back and forth through the dense mass of nucleons (retaining its identity) a number of times before it comes out. This short paper seeks to get over this shortcoming by deriving principally the Gamow's theory through a slightly alternative approach by avoiding the problematic touching frequency in the original theory.
Alpha-decay half-lives for 104,105,106Te and 108,109,110Xe close above the doubly-magic 100Sn are calculated from systematic double-folding potentials. The derived alpha preformation factors are compared to results for 212,213,214Po and 216,217,218Rn above the doubly-magic 208Pb. Alpha-decay energies of Q_alpha = 5.42 \pm 0.07 MeV and 4.65 \pm 0.15 MeV are predicted for 104Te and 108Xe; the corresponding half-lives are T_{1/2} approx 5 ns for 104Te and of the order of 60 μs for 108Xe. Additionally, the properties of rotational bands in 104Te are analyzed, and the first excited 2+ state in 104T…
In the framework of decay theory of Goldberger and Watson we treat $α$-decay of nuclei as a transition caused by a residual interaction between the initial unperturbed bound state and the scattering states with alpha-particle. The integrable wave function for the $α$-decay is derived. The alpha-particle is described by the wave packet, having small amplitude inside the nucleus and exponentially growing in external region up to the $α$-wave front. The Moshinsky's distortions of the alpha-wave front are analyzed. It is found that the energy of the decaying level does not satisfy commonly accepte…
A simple model to calculate alpha-decay Hindrance Factors is presented. Using deformation values obtained from PES calculations as the only input, Hindrance Factors for the alpha-decay of Rn- and Po-isotopes are calculated. It is found that the intrinsic structure around the Fermi surface determined by the deformed mean field plays an important role in determining the hindrance of alpha-decay. The fair agreement between experimental and theoretical Hindrance Factors suggest that the wave function obtained from the energy minima of the PES calculations contains an important part of the correlat…
Recently synthesis of superheavy nuclei has been achieved in hot fusion reactions. A systematic theoretical calculation of alpha decay half-lives in this region of the periodic system, may be useful in the identification of new nuclei in these type of reactions. Alpha decay half-lives are obtained in the framework of the barrier penetration theory, built with the use of proximity and Coulomb forces. It is estimated from a classical viewpoint, a possible angular momentum maximum value for odd and odd-odd nuclei alpha particles. The masses of the nuclei are obtained from a macro-microscopic mode…
Hartree-Fock calculations with the SKX Skyrme interaction are carried out to obtain alpha-decay Q values for deformed nuclei above $^{208}$Pb assuming axial symmetry. The results for even-even nuclei are compared with experiment and with previous calculations. Predictions are made for alpha-decay Q values and half-lives of even-even super-heavy nuclei. The results are also compared for the recently discovered odd-even chain starting at Z=112 and N=165.
A broad extension of periodic system into the sector of antimatter could be possible sometimes in a remote future. We expect that anti-alpha spontaneous emission from an antimatter nucleus will have the same Q-value and half-life as alpha emission from the corresponding mirror nucleus. This is the consequence of the invariance of binding energy as well as of the surface and Coulomb energy when passing from matter to antimatter nuclei with the the same mass number and the same atomic number. The Q-values and half-lives of all measured up to now 27 cluster radioactivities are given together with…
Scrupulous theoretical study of 8Be nucleus states, both clustered and non-clustered, is performed over a wide range of the excitation energies. The quantities which characterize the degree of the alpha-clustering of these states: spectroscopic factors, cluster form factors as well as the alpha-decay widths are computed in the framework of an accurate ab initio approach developed. Other basic properties of 8Be spectrum: the binding and excitation energies, mean values of the isospin are calculated simultaneously. In the majority of instances the results of the computations turn out to be in a …
The feasibility of alpha and cluster decay from Pt isotopes has been investigated within the framework of Skyrme Hartree-Fock-Bogoliubov theory. Calculation has been carried out for various Skyrme forces. Harmonic oscillator and transformed harmonic oscillator basis are used to solve HFB equations. The role played by shell closure is withal analysed. Half-lives are estimated with the help of Universal Decay Law (UDL). Geiger-Nuttel plots are also plotted and successfully preserves its linear nature.
We present the first fully quantum mechanical calculation of photon radiation accompanying charged particle decay from a barrier resonance. The soft-photon limit agrees with the classical results, but differences appear at next-to-leading-order. Under the conditions of alpha-decay of heavy nuclei, the main contribution to the photon emission stems from Coulomb acceleration and may be computed analytically. We find only a small contribution from the tunneling wave function under the barrier.
We present a quasiclassical theory of alpha decay accompanied by bremsstrahlung with a special emphasis on the case of 210Po, with the aim of finding a unified description that incorporates both the radiation during the tunneling through the Coulomb wall and the finite energy E_gamma of the radiated photon up to E_gamma on the order of Q_alpha/sqrt(eta), where Q_alpha is the alpha-decay Q-value and eta is the Sommerfeld parameter. The corrections with respect to previous quasiclassical investigations are found to be substantial, and excellent agreement with a full quantum mechanical treatment …
The $α$-decay chains of $^{288-287}115$ are studied along with the possible cluster decay modes by using the preformed cluster model (PCM). The calculated $α$-decay half-lives are compared with experimental data and other model calculations. The calculated Q-values, penetration probabilities and preformation probabilities factors for $α$-decay suggest that $^{283}_{170}113$,$^{287}_{172}115$ and $^{272}_{165}107$ parent nuclei are more stable against the $α$-decay. These alpha decay chains are further explored for the possibilities of cluster decay. Decay half lives of different cluster from d…
A new version of the semiempirical formula based on fission approach of alpha decay is derived, by using the optimum values of the fitting parameters determined for even-even nuclei, combined with hindrance factors for even-odd, odd-even, and odd-odd nuclides. The deviations from experimental data for two regions of nuclear chart (493 alpha emitters with Z=52-118 and 142 transuranium nuclei including superheavies (Z=92-118), respectively) are compared with those obtained by using the universal curve and the Viola-Seaborg semiempirical relationship.
The pairing corrections, the single particle occupation numbers, are investigated within density-dependent delta interaction formalism for pairing residual interactions. The potential barrier is computed in the framework of the macroscopic-microscopic model. The microscopic part is based on the Woods-Saxon two center shell model. The alpha-decay of a superheavy element is treated, by paying a special attention to the region of the scission configurations. The sequence of nuclear shapes follows the superasymmetric fission path for alpha decay. It was found that the pairing gaps of the states th…
Alpha emission from a nucleus is a fundamental decay process in which the alpha particle formed inside the nucleus tunnels out through the potential barrier. We describe alpha decay of $^{212}$Po and $^{104}$Te by means of the configuration interaction approach. To compute the preformation factor and penetrability, we use the complex-energy shell model with a separable T=1 interaction. The single-particle space is expanded in a Woods-Saxon basis that consists of bound and unbound resonant states. Special attention is paid to the treatment of the norm kernel appearing in the definition of the f…
A microscopic calculation of $α$-cluster preformation probability and $α$ decay width in the typical $α$ emitter $^{212}$Po is presented. Results are obtained by improving a recent approach to describe $α$ preformation in $^{212}$Po [Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the $^{208}$ Pb core, the calculated alpha decay width of $^{212}$Po agrees fairly well with the measured one.
The Oklo data constrain the depth of the nuclear potential well to a small margin of error, determined by various unknowns, such as the reactor temperature. However, we show that even these small variations could allow the U-238 half-life to vary by more than one order of magnitude.
Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. Whether these fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo alpha-decay in a very short time remains an open question. Alpha-decay half lives of nuclei with 130 < Z < 100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survive…
Nuclear radial distance is a prerequisite for generating any alpha-decay half-life formula by taking a suitable effective potential. We study the emission process of alpha particles from an isolated quasi-bound state generated by an effective potential to a scattering state. The effective potential is expressed in terms of Frahn form of potential which is exactly solvable and an analytical expression for half-life is obtained in terms of Coulomb function, wave function and the potential. We then derive a closed form expression for the decay half-life in terms of the parameters of the potential…
$α$ decay is treated microscopically, where the unstable mother nucleus and residual daughter nucleus are described using HFB wave functions, obtained with the Skyrme effective interaction. From these wave functions the amplitude for forming $α$ particles in the mother nucleus is computed. Two different Skyrme parametrizations with different pairing properties are compared, and we find good agreement with experiment for relative decay rates in both cases. The absolute values of the decay rates are under-estimated.
In this work, the $β$-stable region for Z $\geq$ 90 is proposed. The calculated $β$-stable nuclei in the $β$-stable region are in good agreement with the ones obtained by Möller \emph{et al}.. The half-lives of the nuclei close to the $β$-stable region are calculated and the competition between $α$-decay and $β$-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The predictions for half-lives and decay modes of the nuclei with Z = 107$-$110 are presented.
We present a microscopic calculation of alpha-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The alpha-cluster formation is found to be particularly sensitive to the interplay of the mean field felt by the alpha-cluster and the Pauli blocking as a consequence of antisymmetrization. The striking feature of alpha-cluster formation probability across the major shell closures of 82 protons and 126 neutrons is reproduced. The shell (or subshell) effects on the alpha-clus…
To find candidates for long-lived high-K isomers in even-even Z=106-112 superheavy nuclei we study dominant alpha-decay channel of two- and four-quasi-particle configurations at a low excitation. Energies are calculated within the microscopic - macroscopic approach with the deformed Woods-Saxon potential. Configurations are fixed by a standard blocking procedure and their energy found by a subsequent minimization over deformations. Different excitation energies of a high-K configuration in parent and daughter nucleus seem particularly important for a hindrance of the alpha-decay. A strong hind…
Alpha-decay energies for several chains of super-heavy nuclei are calculated within the self-consistent mean-field approach by using the Fayans functional FaNDF$^0$. They are compared to the experimental data and predictions of two Skyrme functionals, SLy4 and SkM*, and of the macro-micro method as well. The corresponding lifetimes are calculated with the use of the semi-phenomenological formulas by Parkhomenko and Sobiczewski and by Royer and Zhang.
An intense study of the alpha decay properties of the isotopes of superheavy element Z=113 have been performed within the Coulomb and proximity potential model for deformed nuclei (CPPMDN) within the wide range 255 l.e. A l.e. 314. The predicted alpha decay half lives of $^{278}$113 and $^{282}$113 and the alpha half lives of their decay products are in good agreement with the experimental data. 6{α) chains and 4α chains predicted respectively for $^{278}$113 and $^{282}$113 are in agreement with the experimental observation. Our study shows that the isotopes in the mass range 278 l.e. A l.e. …
In this work, we expand upon our previous study, the effect of surface vibrations (low-lying vibrational states) on the calculation of penetration probability in alpha decay of spherical isotopes [Phys.Rev.C91,034611(2015)]. To this aim, the Coulomb and proximity potential model, taking in to account the ground state deformations of the involved nuclei along with the surface vibrations in the daughter nucleus, is used to evaluate the alpha decay probability. The results are compared with those obtained by spherical potential barrier, which shows the dramatic effect of employing the ground stat…
Using the exponentially diffuse boundary potential of Green and Lee (1955), we develop a Mathematica notebook to treat alpha decay by using the complex energy approach of Preston (1947), as modified by Pierronne and Marquez (1978). Our approach allows the potential to change slowly from the well depth of the interior of the nucleus to the top of the Coulomb barrier, rather than the sudden step of the simple square well used by Pierronne and Marquez. Recent interest in possible variation in coupling constants such as the strong coupling alpha_s motivates us to develop this algorithm which can a…
The consecutive microscopic solution is presented of the problem of tunneling of a particle through a potential barrier. The method is applied to the alpha and proton decay of compound systems formed in fusion reaction. Appearance of the peaks in the spectrum of emitted particles is predicted. The peaks correspond to quasistationary states inside the potential barrier.
Artificial neural networks are trained by a standard backpropagation learning algorithm with regularization to model and predict the systematics of -decay of heavy and superheavy nuclei. This approach to regression is implemented in two alternative modes: (i) construction of a statistical global model based solely on available experimental data for alpha-decay half-lives, and (ii) modeling of the {\it residuals} between the predictions of state-of-the-art phenomenological model (specifically, the effective liquid-drop model (ELDM)) and experiment. Analysis of the results provide insights on th…
It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and odd-odd isotopes can be also well described when ones introduces an additional hindrance factor. Similar model based on the W. J. Swiatecki idea from 1955 is developed to reproduce the spontaneous fission half-lives of transactinide nuclei. The achieved accuracy of reproduction of the data is better than that obtained in more advanced theories.
A spatial-time method of description of alpha-decay of a nucleus is presented. The method is based on the quantum mechanical model of the alpha-decay of a compound nuclear system with the barrier. alpha-decay dynamics is described on the basis of multiple internal reflections of wave packets from boundaries of the decay barrier. The method allows to study this process in details at any time moment or point of space. According to the method, some time before the time moment of the nuclear decay the nucleus makes oscilations. In the calculations of the time duration of the alpha-decay of the com…
The alpha-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated based on a unified fission model (UFM) where a new method to calculate the assault frequency of alpha-emission is used. The excellent agreement with the experimental data indicates the UFM is a useful tool to investigate these alpha-decays. It is found that the half-lives become more and more insensitive to the Q_alpha values as the atomic number increases on the whole, which is favorable for us to predict the half-lives of SHN. In addition, a formula is suggested to compute the Q_alpha values for the n…
The alpha decay half-lives of the recently produced isotopes of the 112, 114, 116 and 118 nuclei and decay products have been calculated in the quasi-molecular shape path using the experimental Qalpha value and a Generalized Liquid Drop Model including the proximity effects between nucleons in the neck or the gap between the nascent fragments. Reasonable estimates are obtained for the observed alpha decay half-lives. The results are compared with calculations using the Density-Dependent M3Y effective interaction and the Viola-Seaborg-Sobiczewski formulae. Generalized Liquid Drop Model predicti…
It is suggested that superfluid helium (condensate of 4-He atoms) may stimulate nuclear alpha-decay in a situation when an alpha-emitter moves through superfluid helium with fine-tuned velocity, so that the backward-emitted alpha-particle is at rest in the laboratory frame. It is shown that the probability of stimulated alpha-decay in this case may be sizable enough to be detected.
The 15O(alpha,gamma)19Ne reaction is one of two routes for breakout from the hot CNO cycles into the rp process in accreting neutron stars. Its astrophysical rate depends critically on the decay properties of excited states in 19Ne lying just above the 15O + alpha threshold. We have measured the alpha-decay branching ratios for these states using the p(21Ne,t)19Ne reaction at 43 MeV/u. Combining our measurements with previous determinations of the radiative widths of these states, we conclude that no significant breakout from the hot CNO cycle into the rp process in novae is possible via 15O(a…
The ratio of the alpha-decay widths of a bare nucleus and the related atom is calculated. Both the change of the form and thus the penetrability of the potential barrier and the effect of reflection in the classically-allowed region appearing due to the electron shell are taken into account in the calculations of this ratio. The contribution of each of these two effects is of one and the same order of magnitude. For long-lived radioactive samples the values of the total effect turn out to be somewhat below 1 percent.
The alpha decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calc…
A high-statistics measurement of bremsstrahlung emitted in the alpha decay of 210Po has been performed, which allows to follow the photon spectra up to energies of ~ 500 keV. The measured differential emission probability is in good agreement with our theoretical results obtained within the quasi classical approximation as well as with the exact quantum mechanical calculation. It is shown that due to the small effective electric dipole charge of the radiating system a significant interference between the electric dipole and quadrupole contributions occurs, which is altering substantially the a…
Theoretical estimates of $α$-decay half lives of several nuclei in the decay from element 113 are presented. Calculations in a WKB framework using DDM3Y interaction and experimental Q-values are in good agreement with the experimental data. Half life calculations are found to be quite sensitive to the Q-values and angular momenta transfers. Calculated decay lifetime decreases, owing to more penetrability as well as thinner barrier, as Q-value increases. Deviations to this predominant behaviour observed in some recent experimental data may be attributed to non zero spin-parities in some cases.
The 15O(alpha,gamma)19Ne reaction is one of two known routes for breakout from the hot CNO cycles into the rp process. Its astrophysical rate depends on the decay properties of excited states in 19Ne lying just above the 15O + alpha threshold. We have measured the alpha-decay branching ratios for these states using the p(21Ne,t)19Ne reaction at 43 MeV/u. Combining our branching ratio measurements with previous determinations of the radiative widths of these states, we calculate the astrophysical rate of 15O(alpha,gamma)19Ne. Using this reaction rate, we perform hydrodynamic calculations of nov…
It has been recently suggested that one might drastically shorten the alpha lifetime of nuclear waste products, if these are embedded in metals at low temperatures. Using quantum mechanical tunneling arguments, we show that such an effect is likely to be very small, if present at all.
A quantum mechanical model for the description of the alpha-decay of heavy nuclei with accompanying photons emission is presented. The model is based on a quantum mechanical one-particle model of alpha-decay through a decay barrier. The bremsstrahlung spectrum calculation employs multipole expansion of the vector potential of the Coulomb field of the daughter nucleus and takes into account the dependence on the angle between the directions of the alpha-particle propagation and the photon emission. Spectra of 210Po are obtained for the angles 25 and 90, and the best agreement with the experimen…
Using our previous approach to electromagnetic emission during tunneling, an explicit, essentially classical, formula describing the bremsstrahlung spectrum in alpha decay is derived. The role of tunneling motion in photon emission is discussed. The shape of the spectrum is a universal function of the ratio Eg/Eo , where Eg is the photon energy and Eo is a characteristic energy depending only on the nuclear charge and the energy of the alpha particle.
An assumption of isospin symmetry permits the determination of sin(2 alpha) from the experimental study of B\to pi pi decays. Isospin, however, is merely an approximate symmetry; its breaking predicates a theoretical systematical error sigma_α^{\rm IB} in the extraction of alpha. We focus on the impact of π^0-η,η^\prime mixing, as well as the manner in which it is amenable to empirical constraint, and determine that σ_α^{\rm IB} can potentially be controlled to {\cal O}(1^\circ).
