Expiation.  Redemption.  In Hindu religion, most kinds of sins can be cleared by doing Praayashchit. Praayashchit means = Praaya means Tapas (deep meditation) and Chit means definitely .That is for the sin or fault committed by us, if we do redemptive acts like Krichhra Vrat, Sharanaagathi (surrender) as per Shaastra, it is believed that the sin would be removed. These acts of redemption are called Praayashchit. This Praayashchit is mostly in the form of fast, donation, Yagya etc. In classics like Manu Smriti, Paraashar Smriti and other sources the redemption for doing voluntary abortion are as following;

(1) performance of Krichhra Chandraayan Vrat (which is a bit tough for today's world for householders. ....one takes one handful of rice as whole day's food on 1st lunar day and 2 handfuls on 2nd Tithi and 15 handfuls on Full Moon day.... completing the fast on New Moon day... There is no bar in drinking pure water... (but drinking tea , coffee or milk, yogurt, Sharbat etc prohibited) for one year. Beside the condition on food, there is condition that one should try his best not to tell a single lie or commit any untruthful action. Unless one is very well versed in Soorya-bhed Pranaayaam... (art of reducing the metabolic rate of burning or spending our body energies through Praanaayaam) it becomes very tough to continue this Vrat without neglecting the general household duties. Everyday the person takes the food (handful size = equal to the average size of a hen's egg) after seeing the Moon. Since this Vrat follows movement of Moon... this is called Chandraayan = Chandra + Ayan (movement). The person should take the name of Lord Krishn in any form he likes throughout the day ... meditating upon Krishn. Even childless people get children after performance of this Vrat even after doctors have declared them as impotent or barren. Such is the wonderful grace of the Lord .

(2) Regular observance of Upavaas (meaning staying close to Lord by doing meditation and taking Lord's name) eating light food and drinks, maintaining truthfulness in behavior on all 24 Ekaadashee days of the year for 11 years.

(3) Doing regular Praanaayaam for 48 minutes in the morning and in the evening for 1 years at least.

(4) Doing regular recitation and meditation on Gaayatree mantra for 48 minutes a day for 3 years.

Results of Doing Praayashchit
There are two results of Praayashchit. One is that the sinner will not suffer in hell after death. He also can have good interaction with every one in this world when he is alive. But if he has committed the five great sins, even if he carries out the Praayashchit, no interaction should be there with him. No body should have any dealings with him. For people who do Upa-Paatak intentionally, they should do double the amount of Praayashchit. If this is done even for them there is no suffering in hell and people will move with them. If Upa-Paatak are done unintentionally, Praayashchit can be done just by reading Ved, but if done intentionally Praayashchit rituals should be carried out.

Because Praayashchit acts after death are banned in the Kali age, for the acts of passion done intentionally resulting in a Mahaa-Paatak, the suffering for hell is bound to be there. But if he does the 12 year Saadhya Prayashchit, other people can move with him.

Mantras and Vrat for Praayashchit
[Agni Puraan, Ch 171, p 343-344]

Pushkar Jee said to Parashuraam Jee - "Now I tell you about the Praayashchit of Gupt (secret, or hidden) sins.
(1) Who does Jaap of Purush Sookt for one month, his all Paap are washed away.
(2) Aghamarshan Mantra Jaap frees from all kinds of sins.
(3) Ved Mantra, Vaayu Sookt, Yam Sookt, and Gaayatree Mantra Jap washes all sins of the person.
(4) Paraashar says that Chaandraayan, Yavak Krichchhra, Tulaa Purush Daan, Gau Vrat and taking care of cows are normal redemptive acts for all sins. [see various Types of Vrat]
(5) If we chant the Shree Rudra Mantra, 11 times, even if we have committed great sins, we would get rid of all sins.